×

zbMATH — the first resource for mathematics

Friedman, Avner

Compute Distance To:
Author ID: friedman.avner Recent zbMATH articles by "Friedman, Avner"
Published as: Friedman, A.; Friedman, Avner
External Links: MGP · Wikidata · GND
Documents Indexed: 550 Publications since 1956, including 43 Books
Biographic References: 1 Publication
all top 5

Co-Authors

211 single-authored
43 Caffarelli, Luis Ángel
35 Hu, Bei
12 Chen, Xinfu
12 Velázquez, Juan J. L.
11 Reitich, Fernando
10 Alt, Hans Wilhelm
8 DiBenedetto, Emmanuele
8 McLeod, John Bryce
8 Yakubu, Abdul-Aziz
7 Fontelos López, Marco Antonio
7 Hao, Wenrui
6 Bazaliy, Borys V.
6 Cui, Shangbin
6 Kim, Yangjin
6 Ledzewicz, Urszula
6 Siewe, Nourridine
5 Anderson, Robert F. V.
5 Devinatz, Allen
5 Jensen, Robert E.
5 Lai, Xiulan
5 Pinsky, Mark Allan
5 Xue, Chuan
4 Bellout, Hamid
4 Bensoussan, Alain
4 Brézis, Haïm
4 Craciun, Gheorghe
4 Huang, Chaocheng
4 Kao, Chiu-Yen
4 Littman, Walter
4 Shinbrot, Marvin
4 Torelli, Alessandro
4 Turkington, Bruce E.
4 Vogelius, Michael S.
3 Aguda, Baltazar D.
3 Elliott, Charles M.
3 Herrero, Miguel Ángel
3 Huang, Shaoyun
3 Jiang, Lishang
3 Lacey, Andrew A.
3 Lam, King-Yeung
3 Liu, Yong
3 Ross, David Stuart
2 Baiocchi, Claudio
2 Bazaliy, Yaroslaw B.
2 Chen, Duan
2 Dembele, Bassidy
2 Elliott, Robert James
2 Evans, Lawrence Craig
2 Goel, Pranay
2 Green, J. Edward F.
2 Isakov, Victor M.
2 Jain, Harsh Vardhan
2 Kashdan, Eugene
2 Kaur, Balveen
2 Kinderlehrer, David
2 Lesinski, Gregory B.
2 Liao, Kang-Ling
2 Liu, Wenxiong
2 Lo, Wing-Cheong
2 Lungu, Edward M.
2 Marsh, Clay B.
2 Oswald, Luc
2 Ou, Biao
2 Pozzi, Gianni Arrigo
2 Satoskar, Abhay R
2 Schättler, Heinz Michael
2 Shih, Chih-Wen
2 Tao, Youshan
2 Tello, José Ignacio
2 Tzavaras, Athanasios E.
2 Véron, Laurent
2 Vogel, Thomas Irvin
2 Yong, Jiongmin
2 Zhang, Jianhua
1 Aronson, Donald G.
1 Arsenescu, Razvan I.
1 Bai, Xue-Feng
1 Banasiak, Jacek
1 Bao, Gang
1 Barbu, Viorel
1 Bassom, Andrew P.
1 Bell, Jonathan
1 Bemelmans, Josef
1 Bernis, Francisco
1 Borisovich, Andreĭ Yur’evich
1 Borisyuk, Alla
1 Boushaba, Khalid
1 Brokate, Martin
1 Brown, Anthony K.
1 Bruno, Oscar P.
1 Budd, Christopher John
1 Caligiuri, Michael A.
1 Chechkin, Gregory Aleksandrovich
1 Chiocca, E. Antonio
1 Chou, Ching-Shan
1 Conley, Elizabeth
1 Conwell, Darwin L.
1 Coskun, Huseyin
1 Crouser, Elliott D.
1 Day, Judy D.
...and 93 more Co-Authors
all top 5

Serials

48 Journal of Differential Equations
46 Transactions of the American Mathematical Society
38 Archive for Rational Mechanics and Analysis
34 Indiana University Mathematics Journal
26 Journal of Mathematical Analysis and Applications
21 Journal of Mathematics and Mechanics
20 SIAM Journal on Mathematical Analysis
13 Mathematical Biosciences and Engineering
12 Bulletin of Mathematical Biology
12 Communications in Partial Differential Equations
12 Journal of Theoretical Biology
11 The IMA Volumes in Mathematics and its Applications
10 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
10 Pacific Journal of Mathematics
10 SIAM Journal on Control and Optimization
10 Nonlinear Analysis. Theory, Methods & Applications
8 Discrete and Continuous Dynamical Systems. Series B
7 SIAM Journal on Applied Mathematics
6 Journal of Mathematical Biology
5 Duke Mathematical Journal
5 Proceedings of the American Mathematical Society
5 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
5 Proceedings of the National Academy of Sciences of the United States of America
5 Bulletin of the American Mathematical Society
4 Mathematical Biosciences
4 Journal of Functional Analysis
4 Journal für die Reine und Angewandte Mathematik
4 Kiberneticheskiĭ Sbornik. Novaya Seriya
4 European Journal of Applied Mathematics
4 Interfaces and Free Boundaries
3 Journal d’Analyse Mathématique
3 Acta Mathematica
3 Illinois Journal of Mathematics
3 Michigan Mathematical Journal
3 Notices of the American Mathematical Society
3 Lecture Notes in Mathematics
2 Communications on Pure and Applied Mathematics
2 American Journal of Mathematics
2 Annali di Matematica Pura ed Applicata. Serie Quarta
2 Annales Polonici Mathematici
2 Mathematics of Operations Research
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Quarterly of Applied Mathematics
2 Asymptotic Analysis
2 SIAM Review
2 Discrete and Continuous Dynamical Systems
2 Multiscale Modeling & Simulation
2 Journal of Biological Dynamics
2 Mathematical Modelling of Natural Phenomena
2 Lecture Notes on Mathematical Modelling in the Life Sciences
2 Oxford Graduate Texts
1 Inverse Problems
1 Israel Journal of Mathematics
1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV)
1 Reviews of Modern Physics
1 Rocky Mountain Journal of Mathematics
1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
1 Applied Mathematics and Optimization
1 Journal of the Faculty of Science. Section I A
1 Journal of Optimization Theory and Applications
1 Chinese Annals of Mathematics. Series B
1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
1 Journal de Mathématiques Pures et Appliquées. Neuvième Série
1 Journal of Non-Newtonian Fluid Mechanics
1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
1 Comptes Rendus de l’Académie des Sciences. Série I
1 Bollettino della Unione Matemàtica Italiana. Serie VII. B
1 Continuum Mechanics and Thermodynamics
1 Applied Mathematics. Series A (Chinese Edition)
1 Finance and Stochastics
1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales (España)
1 SIAM Journal on Control
1 Regional Conference Series in Mathematics
1 Mathematics in Industry
1 Networks and Heterogeneous Media
1 Science China. Mathematics
1 Philosophical Transactions A. Royal Society of London
1 CBMS Regional Conference Series in Mathematics
1 Springer Undergraduate Texts in Mathematics and Technology
all top 5

Fields

310 Partial differential equations (35-XX)
125 Biology and other natural sciences (92-XX)
73 Fluid mechanics (76-XX)
68 Calculus of variations and optimal control; optimization (49-XX)
39 Probability theory and stochastic processes (60-XX)
33 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
28 Mechanics of deformable solids (74-XX)
26 General and overarching topics; collections (00-XX)
25 Systems theory; control (93-XX)
19 Optics, electromagnetic theory (78-XX)
18 Ordinary differential equations (34-XX)
16 Classical thermodynamics, heat transfer (80-XX)
12 Statistics (62-XX)
11 Operations research, mathematical programming (90-XX)
10 Potential theory (31-XX)
7 Dynamical systems and ergodic theory (37-XX)
7 Operator theory (47-XX)
6 Statistical mechanics, structure of matter (82-XX)
5 Integral equations (45-XX)
5 Numerical analysis (65-XX)
3 Functional analysis (46-XX)
3 Global analysis, analysis on manifolds (58-XX)
2 History and biography (01-XX)
2 Real functions (26-XX)
2 Measure and integration (28-XX)
2 Special functions (33-XX)
2 Mechanics of particles and systems (70-XX)
2 Quantum theory (81-XX)
2 Astronomy and astrophysics (85-XX)
2 Geophysics (86-XX)
1 Combinatorics (05-XX)
1 Functions of a complex variable (30-XX)
1 Difference and functional equations (39-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Differential geometry (53-XX)
1 General topology (54-XX)
1 Information and communication theory, circuits (94-XX)

Publications by Year

Citations contained in zbMATH Open

456 Publications have been cited 11,114 times in 8,197 Documents Cited by Year
Partial differential equations of parabolic type. Zbl 0144.34903
Friedman, A.
1964
Partial differential equations. Zbl 0224.35002
Friedman, Avner
738
1969
Stochastic differential equations and applications. Vol. 1. Zbl 0323.60056
Friedman, Avner
435
1975
Variational principles and free-boundary problems. Zbl 0564.49002
Friedman, Avner
390
1982
Blow-up of positive solutions of semilinear heat equations. Zbl 0576.35068
Friedman, Avner; McLeod, Bryce
342
1985
Stochastic differential equations and applications. Vol. 2. Zbl 0323.60057
Friedman, Avner
278
1976
Differential games. Zbl 0229.90060
Friedman, Avner
173
1971
Higher order nonlinear degenerate parabolic equations. Zbl 0702.35143
Bernis, Francisco; Friedman, Avner
172
1990
Variational problems with two phases and their free boundary. Zbl 0844.35137
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
166
1984
Hölder estimates for non-linear degenerate parabolic systems. Zbl 0549.35061
DiBenedetto, Emmanuele; Friedman, Avner
154
1985
Classes of solutions of linear systems of partial differential equations of parabolic type. Zbl 0092.31002
Friedman, Avner
148
1957
Analysis of a mathematical model for the growth of tumors. Zbl 0944.92018
Friedman, Avner; Reitich, Fernando
131
1999
Nonlinear parabolic equations involving measures as initial conditions. Zbl 0527.35043
Brézis, Haïm; Friedman, Avner
128
1983
The Stefan problem in several space variables. Zbl 0162.41903
Friedman, A.
95
1968
Generalized functions and partial differential equations. Zbl 0116.07002
Friedman, A.
92
1963
Convexity of solutions of semilinear elliptic equations. Zbl 0599.35065
Caffarelli, Luis A.; Friedman, Avner
89
1985
Variational principles and free-boundary problems. Reprint. Zbl 0671.49001
Friedman, Avner
79
1988
A free boundary problem arising in a model of wound healing. Zbl 0972.35193
Chen, Xinfu; Friedman, Avner
75
2000
Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions. Zbl 0631.35041
Friedman, Avner
72
1986
Regularity of the free boundary of a gas flow in an \(n\)-dimensional porous medium. Zbl 0439.76085
Caffarelli, Luis A.; Friedman, Avner
68
1980
Symmetry-breaking bifurcation of analytic solutions to free boundary problems: An application to a model of tumor growth. Zbl 0983.35019
Friedman, Avner; Reitich, Fernando
64
2001
Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence. Zbl 0684.35087
Friedman, Avner; Vogelius, Michael
64
1989
Regularity of solutions of nonlinear degenerate parabolic systems. Zbl 0527.35038
DiBenedetto, Emmanuele; Friedman, Avner
64
1984
Blow-up of solutions of nonlinear degenerate parabolic equations. Zbl 0619.35060
Friedman, Avner; McLeod, Bryce
63
1986
Foundations of modern analysis. Zbl 0198.07601
Friedman, Avner
63
1970
Analysis of a mathematical model of the effect of inhibitors on the growth of tumors. Zbl 0998.92022
Cui, Shangbin; Friedman, Avner
62
2000
Foundations of modern analysis. Reprint of the 1970 orig. Zbl 0557.46001
Friedman, Avner
59
1982
The asymptotic behavior of gas in an \(n\)-dimensional porous medium. Zbl 0447.76076
Friedman, Avner; Kamin, Shoshana
59
1980
Parabolic variational inequalities in one space dimension and smoothness of the free boundary. Zbl 0295.35045
Friedman, Avner
58
1975
Optimal stochastic switching and the Dirichlet problem for the Bellman equation. Zbl 0425.35046
Evans, Lawrence C.; Friedman, Avner
55
1979
A one phase Stefan problem. Zbl 0334.49002
Friedman, Avner; Kinderlehrer, David
54
1975
Free boundary problems for parabolic equations. I: Melting of solids. Zbl 0089.07801
Friedman, Avner
53
1959
Bifurcation from stability to instability for a free boundary problem arising in a tumor model. Zbl 1087.92039
Friedman, Avner; Hu, Bei
52
2006
Mathematical analysis of a model for the initiation of angiogenesis. Zbl 1020.35030
Fontelos, Marco A.; Friedman, Avner; Hu, Bei
52
2002
Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations. Zbl 0593.35047
Caffarelli, Luis A.; Friedman, Avner
52
1985
Mathematical analysis and challenges arising from models of tumor growth. Zbl 1135.92013
Friedman, Avner
50
2007
Remarks on the maximum principle for parabolic equations and its applications. Zbl 0103.06403
Friedman, Avner
50
1958
A free boundary problem for quasi-linear elliptic equations. Zbl 0554.35129
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
49
1984
Volterra integral equations in Banach space. Zbl 0147.12302
Friedman, A.; Shinbrot, M.
49
1967
On the regularity of the solutions of nonlinear elliptic and parabolic systems of partial differential equations. Zbl 0078.27702
Friedman, Avner
49
1958
A free boundary problem for an elliptic-hyperbolic system: an application to tumor growth. Zbl 1054.35144
Chen, Xinfu; Friedman, Avner
48
2003
Determining cracks by boundary measurements. Zbl 0697.35165
Friedman, Avner; Vogelius, Michael
48
1989
The obstacle problem for the biharmonic operator. Zbl 0405.31007
Caffarelli, Luis A.; Friedman, Avner
46
1979
Stability of solutions of chemotaxis equations in reinforced random walks. Zbl 1025.35005
Friedman, Avner; Tello, J. Ignacio
45
2002
Analysis of a mathematical model of the growth of necrotic tumors. Zbl 0984.35169
Cui, Shangbin; Friedman, Avner
45
2001
Continuity of the density of a gas flow in a porous medium. Zbl 0425.35060
Caffarelli, Luis A.; Friedman, Avner
45
1979
The boundary-value problem in domains with very rapidly oscillating boundary. Zbl 0938.35049
Chechkin, Gregory A.; Friedman, Avner; Piatnitski, Andrey L.
43
1999
Symmetry-breaking bifurcations of free boundary problems in three dimensions. Zbl 1054.35145
Fontelos, Marco A.; Friedman, Avner
42
2003
On the properties of a singular Sturm-Liouville equation determined by its spectral functions. Zbl 0091.08102
Friedman, Avner
42
1957
Stochastic differential equations and applications. Reprint of the 1975 and 1976 original editions. Zbl 1113.60003
Friedman, Avner
41
2006
Analysis of a mathematical model of tumor lymphangiogenesis. Zbl 1060.92036
Friedman, Avner; Lolas, Georgios
41
2005
A hierarchy of cancer models and their mathematical challenges. Zbl 1052.35094
Friedman, Avner
41
2004
A single point blow-up for solutions of semilinear parabolic systems. Zbl 0648.35042
Friedman, Avner; Giga, Yoshikazu
40
1987
Asymptotic stability for a free boundary problem arising in a tumor model. Zbl 1136.35106
Friedman, Avner; Hu, Bei
39
2006
The free boundary of a semilinear elliptic equation. Zbl 0552.35079
Friedman, Avner; Phillips, Daniel
39
1984
Stochastic differential games. Zbl 0208.39402
Friedman, Avner
39
1972
Partial differential equations of parabolic type. Zbl 0173.12701
Friedman, A.
39
1968
Stability and instability of Liapunov-Schmidt and Hopf bifurcation for a free boundary problem arising in a tumor model. Zbl 1161.35059
Friedman, Avner; Hu, Bei
37
2008
A free boundary problem for an elliptic-parabolic system: application to a model of tumor growth. Zbl 1031.35151
Bazaliy, Borys V.; Friedman, Avner
37
2003
The time-harmonic Maxwell equations in a doubly periodic structure. Zbl 0759.35046
Dobson, David; Friedman, Avner
37
1992
Extinction properties of semilinear heat equations with strong absorption. Zbl 0655.35050
Friedman, Avner; Herrero, Miguel A.
37
1987
The blow-up boundary for nonlinear wave equations. Zbl 0638.35053
Caffarelli, Luis A.; Friedman, Avner
37
1986
Bifurcation for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1136.35107
Friedman, Avner; Hu, Bei
35
2007
Optimal control for variational inequalities. Zbl 0604.49007
Friedman, Avner
35
1986
Regularity of the free boundary for the one-dimensional flow of gas in a porous medium. Zbl 0439.76084
Caffarelli, Luis A.; Friedman, Avner
34
1979
On integral equations of Volterra type. Zbl 0134.31502
Friedman, A.
34
1963
Nonlinear stability of a quasi-static Stefan problem with surface tension: a continuation approach. Zbl 1072.35208
Reitich, Fernando; Friedman, Avner
33
2001
The shape of axisymmetric rotating fluid. Zbl 0439.35068
Caffarelli, Luis A.; Friedman, Avner
33
1980
On the uniqueness in the inverse conductivity problem with one measurement. Zbl 0703.35165
Friedman, Avner; Isakov, Victor
32
1989
The ill-posed Hele-Shaw model and the Stefan problem for supercooled water. Zbl 0621.35102
DiBenedetto, Emmanuele; Friedman, Avner
32
1984
Asymptotic estimates for the plasma problem. Zbl 0466.35033
Caffarelli, Luis A.; Friedman, Avner
32
1980
Nonlinear variational inequalities and differential games with stopping times. Zbl 0297.90120
Bensoussan, Alain; Friedman, Avner
32
1974
Interior estimates for parabolic systems of partial differential equations. Zbl 0082.30402
Friedman, Avner
31
1958
Addendum to “Hölder estimates for nonlinear degenerate parabolic systems”. Zbl 0595.35065
DiBenedetto, Emmanuelle; Friedman, Avner
30
1985
Differentiability of the blow-up curve for one dimensional nonlinear wave equations. Zbl 0593.35055
Caffarelli, Luis A.; Friedman, Avner
30
1985
Jets with two fluids. I. One free boundary. Zbl 0551.76013
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
30
1984
Reinforcement problems for elliptic equations and variational inequalities. Zbl 0434.35079
Brézis, Haïm; Caffarelli, Luis A.; Friedman, Avner
30
1980
Systems of nonlinear wave equations with nonlinear viscosity. Zbl 0685.35070
Friedman, Avner; Nečas, Jindřich
29
1988
Axially symmetric jet flows. Zbl 0515.76017
Alt, H. W.; Caffarelli, L. A.; Friedman, A.
29
1983
Nonzero-sum stochastic differential games with stopping times and free boundary problems. Zbl 0368.93029
Bensoussan, Alain; Friedman, Avner
29
1977
Global existence and asymptotic stability for an elliptic-parabolic free boundary problem: an application to a model of tumor growth. Zbl 1089.35079
Bazaliy, Borys; Friedman, Avner
27
2003
A free boundary problem for a singular system of differential equations: An application to a model of tumor growth. Zbl 1036.34018
Cui, Shangbin; Friedman, Avner
26
2003
Maxwell’s equations in a periodic structure. Zbl 0727.35131
Chen, Xinfu; Friedman, Avner
26
1991
Analysis of a free-boundary tumor model with angiogenesis. Zbl 1344.35172
Friedman, Avner; Lam, King-Yeung
25
2015
Asymmetric jet flows. Zbl 0515.76018
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
25
1982
Vortex rings: existence and asymptotic estimates. Zbl 0497.76031
Friedman, Avner; Turkington, Bruce
25
1981
Blow-up of solutions of nonlinear heat equations. Zbl 0653.35038
Caffarelli, Luis A.; Friedman, Avner
24
1988
Optimal control for parabolic variational inequalities. Zbl 0624.49005
Friedman, Avner
24
1987
One dimensional Stefan problems with nonmonotone free boundary. Zbl 0162.42001
Friedman, A.
24
1968
Isometric embedding of riemannian manifolds into Euclidean spaces. Zbl 0137.14901
Friedman, A.
24
1965
Generalized heat transfer between solids and gases under nonlinear boundary conditions. Zbl 0101.31102
Friedman, Avner
24
1959
Bifurcation from stability to instability for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1122.35013
Friedman, Avner; Hu, Bei
23
2007
Compressible flows of jets and cavities. Zbl 0614.76074
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
23
1985
Stochastic games and variational inequalities. Zbl 0285.90089
Friedman, Avner
23
1973
On the existence of spatially patterned dormant malignancies in a model for the growth of non-necrotic vascular tumors. Zbl 1013.92024
Friedman, Avner; Reitich, Fernando
22
2001
Asymptotic behavior of solutions of \(u_ t=\Delta u^ m\) as \(m\to \infty\). Zbl 0651.35039
Caffarelli, Luis A.; Friedman, Avner
22
1987
Periodic behaviour for the evolutionary dam problem and related free boundary problems. Zbl 0624.35084
DiBenedetto, Emmanuele; Friedman, Avner
22
1986
Jets with two fluids. II: Two free boundaries. Zbl 0588.76017
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
22
1984
Convexity of the free boundary in the Stefan problem and in the dam problem. Zbl 0375.35028
Friedman, Avner; Jensen, Robert
22
1977
Analyticity of the free boundary for the Stefan problem. Zbl 0329.35034
Friedman, Avner
22
1976
Mathematical modeling in scheduling cancer treatment with combination of VEGF inhibitor and chemotherapy drugs. Zbl 1406.92312
Lai, Xiulan; Friedman, Avner
2
2019
Rheumatoid arthritis – a mathematical model. Zbl 1406.92273
Moise, Nicolae; Friedman, Avner
1
2019
The role of exosomes in pancreatic cancer microenvironment. Zbl 1394.92056
Friedman, Avner; Hao, Wenrui
5
2018
Mathematical model of chronic pancreatitis. Zbl 1404.92096
Hao, Wenrui; Komar, Hannah M.; Hart, Phil A.; Conwell, Darwin L.; Lesinski, Gregory B.; Friedman, Avner
4
2017
The role of TNF-\(\alpha\) inhibitor in glioma virotherapy: a mathematical model. Zbl 1362.92034
Ratajczyk, Elzbieta; Ledzewicz, Urszula; Leszczynski, Maciej; Friedman, Avner
4
2017
Granuloma formation in leishmaniasis: a mathematical model. Zbl 1368.92087
Siewe, Nourridine; Yakubu, Abdul-Aziz; Satoskar, Abhay R; Friedman, Avner
3
2017
Mathematical modeling of liver fibrosis. Zbl 1348.92079
Friedman, Avner; Hao, Wenrui
2
2017
Free boundary problems for systems of Stokes equations. Zbl 1357.35298
Friedman, Avner
4
2016
Immune response to infection by Leishmania: a mathematical model. Zbl 1341.92042
Siewe, Nourridine; Yakubu, Abdul-Aziz; Satoskar, Abhay R.; Friedman, Avner
4
2016
Introduction to mathematical biology. Modeling, analysis, and simulations. Zbl 1351.92001
Chou, Ching-Shan; Friedman, Avner
4
2016
Analysis of a free-boundary tumor model with angiogenesis. Zbl 1344.35172
Friedman, Avner; Lam, King-Yeung
25
2015
A mathematical model of atherosclerosis with reverse cholesterol transport and associated risk factors. Zbl 1334.92198
Friedman, Avner; Hao, Wenrui
15
2015
A free boundary problem for steady small plaques in the artery and their stability. Zbl 1322.35181
Friedman, Avner; Hao, Wenrui; Hu, Bei
7
2015
Free boundary problems in biology. Zbl 1353.35291
Friedman, Avner
5
2015
Effects of CCN1 and macrophage content on glioma virotherapy: a mathematical model. Zbl 1335.92040
Jacobsen, Karly; Russell, Luke; Kaur, Balveen; Friedman, Avner
3
2015
A PDE model for the dynamics of trail formation by ants. Zbl 1311.35325
Fontelos, Marco A.; Friedman, Avner
1
2015
A mathematical model for pancreatic cancer growth and treatments. Zbl 1412.92154
Louzoun, Yoram; Xue, Chuan; Lesinski, Gregory B.; Friedman, Avner
15
2014
Mathematical model of sarcoidosis. Zbl 1355.92049
Hao, Wenrui; Crouser, Elliott D.; Friedman, Avner
14
2014
On a multiphase multicomponent model of biofilm growth. Zbl 1288.35388
Friedman, Avner; Hu, Bei; Xue, Chuan
8
2014
Mathematical modeling of biological processes. Zbl 1302.92004
Friedman, Avner; Kao, Chiu-Yen
3
2014
On the stability of steady states in a granuloma model. Zbl 1288.35482
Friedman, Avner; Lam, King-Yeung
3
2014
A Bovine babesiosis model with dispersion. Zbl 1282.92019
Friedman, Avner; Yakubu, Abdul-Aziz
3
2014
Mathematical model of renal interstitial fibrosis. Zbl 1355.92050
Hao, Wenrui; Rovin, Brad H.; Friedman, Avner
1
2014
Modulation of the camp response by \(\mathrm{G}\alpha _i\) and \(\mathrm{G}\beta \gamma \): a computational study of G protein signaling in immune cells. Zbl 1298.92038
Leander, R.; Friedman, A.
1
2014
Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy. Zbl 1277.92013
Jain, Harsh Vardhan; Friedman, Avner
10
2013
Anthrax epizootic and migration: persistence or extinction. Zbl 1303.92116
Friedman, Avner; Yakubu, Abdul-Aziz
10
2013
A two-phase free boundary problem with discontinuous velocity: Application to tumor model. Zbl 1256.35208
Chen, Duan; Friedman, Avner
5
2013
Epidemiological models with seasonality. Zbl 1345.92140
Friedman, Avner
3
2013
Mathematical methods and models in biomedicine. Zbl 1254.92046
Ledzewicz, Urszula (ed.); Schättler, Heinz (ed.); Friedman, Avner (ed.); Kashdan, Eugene (ed.)
3
2013
Mathematical model of the roles of T cells in inflammatory bowel disease. Zbl 1272.92030
Lo, Wing-Cheong; Arsenescu, Razvan I.; Friedman, Avner
2
2013
The role of CD200-CD200R in tumor immune evasion. Zbl 1330.92024
Liao, Kang-Ling; Bai, Xue-Feng; Friedman, Avner
1
2013
The diffusion approximation for linear nonautonomous reaction-hyperbolic equations. Zbl 1276.35014
Friedman, Avner; Hu, Bei; Keener, James P.
1
2013
A mathematical model for cell-induced gel compaction in vitro. Zbl 1257.92018
Green, J. E. F.; Bassom, Andrew P.; Friedman, Avner
1
2013
Host demographic Allee effect, fatal disease, and migration: persistence or extinction. Zbl 1273.34052
Friedman, Avner; Yakubu, Abdul-Aziz
13
2012
PDE problems arising in mathematical biology. Zbl 1260.49001
Friedman, Avner
9
2012
Hypoxia inducible factors-mediated inhibition of cancer by GM-CSF: a mathematical model. Zbl 1267.92043
Chen, Duan; Roda, Julie M.; Marsh, Clay B.; Eubank, Timothy D.; Friedman, Avner
8
2012
Modeling the inhibition of breast cancer growth by GM-CSF. Zbl 1337.92118
Szomolay, Barbara; Eubank, Tim D.; Roberts, Ryan D.; Marsh, Clay B.; Friedman, Avner
6
2012
A three dimensional model of wound healing: analysis and computation. Zbl 1395.92076
Friedman, Avner; Hu, Bei; Xue, Chuan
6
2012
Cancer as multifaceted disease. Zbl 1241.92038
Friedman, A.
4
2012
Conservation laws in mathematical biology. Zbl 1258.35142
Friedman, Avner
3
2012
Asymptotic limit in a cell differentiation model with consideration of transcription. Zbl 1267.34078
Friedman, Avner; Kao, Chiu-Yen; Shih, Chih-Wen
2
2012
Fatal disease and demographic Allee effect: population persistence and extinction. Zbl 1447.92337
Friedman, Avner; Yakubu, Abdul-Aziz
1
2012
A mathematical model for chronic wounds. Zbl 1259.92043
Friedman, Avner; Xue, Chuan
7
2011
Asymptotic analysis for the narrow escape problem. Zbl 1252.35030
Chen, Xinfu; Friedman, Avner
7
2011
Tumor cells proliferation and migration under the influence of their microenvironment. Zbl 1259.92042
Friedman, Avner; Kim, Yangjin
5
2011
Modeling the host response to inhalation anthrax. Zbl 1405.92143
Day, Judy; Friedman, Avner; Schlesinger, Larry S.
3
2011
Analysis of a mathematical model of ischemic cutaneous wounds. Zbl 1217.35195
Friedman, Avner; Hu, Bei; Xue, Chuan
11
2010
Interaction of tumor with its micro-environment: a mathematical model. Zbl 1197.92027
Kim, Yangjin; Friedman, Avner
11
2010
Mathematical model for optimal use of sulfadoxine-pyrimethamine as a temporary malaria vaccine. Zbl 1191.92025
Dembele, Bassidy; Friedman, Avner; Yakubu, Abdul-Aziz
6
2010
Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: a mathematical model and experiments. Zbl 1204.92041
Kim, Yangjin; Wallace, Julie; Li, Fu; Ostrowski, Michael; Friedman, Avner
5
2010
Cell cycle control at the first restriction point and its effect on tissue growth. Zbl 1202.92024
Friedman, Avner; Hu, Bei; Kao, Chiu-Yen
5
2010
Mathematical modeling of preadipocyte fate determination. Zbl 1406.92145
Coskun, Huseyin; Summerfield, Taryn L. S.; Kniss, Douglas A.; Friedman, Avner
1
2010
A mathematical model for pattern formation of glioma cells outside the tumor spheroid core. Zbl 1405.92032
Kim, Yangjin; Lawler, Sean; Nowicki, Michal O.; Chiocca, E. Antonio; Friedman, Avner
17
2009
Free boundary problems associated with multiscale tumor models. Zbl 1172.35080
Friedman, A.
10
2009
Malaria model with periodic mosquito birth and death rates. Zbl 1342.92232
Dembele, Bassidy; Friedman, Avner; Yakubu, Abdul-Aziz
9
2009
Asymptotic phases in a cell differentiation model. Zbl 1173.35590
Friedman, Avner; Kao, Chiu-Yen; Shih, Chih-Wen
5
2009
Stability and instability of Liapunov-Schmidt and Hopf bifurcation for a free boundary problem arising in a tumor model. Zbl 1161.35059
Friedman, Avner; Hu, Bei
37
2008
A multiscale tumor model. Zbl 1157.35501
Friedman, Avner
7
2008
Models of cellular regulation. Zbl 1231.92030
Aguda, Baltazar D.; Friedman, Avner
5
2008
The role of oxygen in tissue maintenance: mathematical modeling and qualitive analysis. Zbl 1152.35524
Friedman, Avner; Hu, Bei
5
2008
Tutorials in mathematical biosciences IV. Evolution and ecology. Tutorials presented at the Mathematical Bioscience Institute (MBI) in the years 2005–2006. Zbl 1130.92002
Friedman, Avner (ed.)
5
2008
The extensional flow of a thin sheet of incompressible, transversely isotropic fluid. Zbl 1141.76009
Green, J. Edward F.; Friedman, Avner
4
2008
A parabolic-hyperbolic quasilinear system. Zbl 1158.35004
Chen, Xinfu; Friedman, Avner; Hu, Bei
2
2008
Mathematical analysis and challenges arising from models of tumor growth. Zbl 1135.92013
Friedman, Avner
50
2007
Bifurcation for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1136.35107
Friedman, Avner; Hu, Bei
35
2007
Bifurcation from stability to instability for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1122.35013
Friedman, Avner; Hu, Bei
23
2007
Uniform convergence for approximate traveling waves in linear reaction-hyperbolic systems. Zbl 1133.35006
Friedman, Avner; Hu, Bei
8
2007
Uniform convergence for approximate traveling waves in linear reaction-diffusion-hyperbolic systems. Zbl 1132.35006
Friedman, Avner; Hu, Bei
3
2007
One-dimensional free boundary problem for actin-based propulsion of Listeria. Zbl 1104.92016
Bazaliy, Borys; Bazaliy, Yaroslaw; Friedman, Avner
2
2007
Bifurcation from stability to instability for a free boundary problem arising in a tumor model. Zbl 1087.92039
Friedman, Avner; Hu, Bei
52
2006
Stochastic differential equations and applications. Reprint of the 1975 and 1976 original editions. Zbl 1113.60003
Friedman, Avner
41
2006
Asymptotic stability for a free boundary problem arising in a tumor model. Zbl 1136.35106
Friedman, Avner; Hu, Bei
39
2006
A free boundary problem for a coupled system of elliptic, hyperbolic, and Stokes equations modeling tumor growth. Zbl 1106.35145
Friedman, Avner
18
2006
Approximate traveling waves in linear reaction-hyperbolic equations. Zbl 1147.35330
Friedman, Avner; Craciun, Gheorghe
12
2006
Homogenization of the cell cytoplasm: the calcium bidomain equations. Zbl 1128.35303
Goel, Pranay; Sneyd, James; Friedman, Avner
8
2006
Tutorials in mathematical biosciences III. Cell cycle, prolifereation, and cancer. Zbl 1122.92030
Friedman, Avner (ed.)
4
2006
Differential games. Reprint of the 1971 original ed. Zbl 1225.91011
Friedman, Avner
3
2006
Analysis of a mathematical model of tumor lymphangiogenesis. Zbl 1060.92036
Friedman, Avner; Lolas, Georgios
41
2005
Symmetry-breaking bifurcations for free boundary problems. Zbl 1079.35012
Borisovich, Andrei; Friedman, Avner
21
2005
A hyperbolic free boundary problem modeling tumor growth: asymptotic behavior. Zbl 1082.35166
Chen, Xinfu; Cui, Shangbin; Friedman, Avner
16
2005
A model of intracellular transport of particles in an axon. Zbl 1068.92016
Friedman, Avner; Craciun, Gheorghe
15
2005
Generalized functions and partial differential equations. Reprint of the 1963 original. Zbl 1121.46001
Friedman, Avner
13
2005
The Hele-Shaw problem with surface tension in a half-plane: a model problem. Zbl 1075.76022
Bazaliy, Borys V.; Friedman, Avner
12
2005
The Hele-Shaw problem with surface tension in a half-plane. Zbl 1076.76028
Bazaliy, Borys V.; Friedman, Avner
10
2005
Tutorials in mathematical biosciences. I: Mathematical neuroscience. Zbl 1062.92008
Borisyuk, Alla; Ermentrout, Bard G.; Friedman, Avner; Terman, David
6
2005
Symmetry-breaking bifurcations for free boundary problems. Zbl 1075.35117
Friedman, Avner
2
2005
Free boundary problems with surface tension conditions. Zbl 1153.35409
Friedman, Avner
1
2005
Mathematical analysis of a modular network coordinating the cell cycle and apoptosis. Zbl 1079.92023
Craciun, Gheorghe; Aguda, Baltazar; Friedman, Avner
1
2005
A hierarchy of cancer models and their mathematical challenges. Zbl 1052.35094
Friedman, Avner
41
2004
Symmetry-breaking bifurcations of charged drops. Zbl 1094.76022
Fontelos, Marco A.; Friedman, Avner
15
2004
Free boundary problems arising in tumor models. Zbl 1162.35460
Friedman, Avner
4
2004
A free boundary problem for an elliptic-hyperbolic system: an application to tumor growth. Zbl 1054.35144
Chen, Xinfu; Friedman, Avner
48
2003
Symmetry-breaking bifurcations of free boundary problems in three dimensions. Zbl 1054.35145
Fontelos, Marco A.; Friedman, Avner
42
2003
A free boundary problem for an elliptic-parabolic system: application to a model of tumor growth. Zbl 1031.35151
Bazaliy, Borys V.; Friedman, Avner
37
2003
Global existence and asymptotic stability for an elliptic-parabolic free boundary problem: an application to a model of tumor growth. Zbl 1089.35079
Bazaliy, Borys; Friedman, Avner
27
2003
A free boundary problem for a singular system of differential equations: An application to a model of tumor growth. Zbl 1036.34018
Cui, Shangbin; Friedman, Avner
26
2003
A hyperbolic free boundary problem modeling tumor growth. Zbl 1040.35143
Cui, Shangbin; Friedman, Avner
18
2003
Nonlinear stability of the Muskat problem with capillary pressure at the free boundary. Zbl 1028.35123
Friedman, Avner; Tao, Youshan
16
2003
Analysis of a model of a virus that replicates selectively in tumor cells. Zbl 1052.92027
Friedman, Avner; Tao, Youshan
14
2003
Mathematical models in photographic science. Zbl 1290.82030
Friedman, Avner; Ross, David S.
2
2003
...and 356 more Documents
all top 5

Cited by 7,867 Authors

204 Friedman, Avner
56 Mu, Chunlai
52 Vazquez, Juan Luis
47 Hu, Bei
47 Winkler, Michael
39 Caffarelli, Luis Ángel
37 Zheng, Sining
35 Galaktionov, Victor Aleksandrovich
34 Shahgholian, Henrik
34 Wang, Mingxin
34 Yi, Fahuai
32 Cui, Shangbin
30 Mao, Xuerong
30 Xu, Shihe
29 Pao, Chia-Ven
29 Tao, Youshan
28 Cannon, John Rozier
28 Liu, Bingchen
26 Chen, Xinfu
26 Lin, Zhigui
25 Fasano, Antonio
24 Li, Fengjie
24 Primicerio, Mario
23 Ammari, Habib M.
23 Peletier, Lambertus Adrianus
22 Diaz Diaz, Jesus Ildefonso
22 Du, Lili
22 Guo, Jong-Shenq
20 Souplet, Philippe
20 Xie, Chunhong
19 Herrero, Miguel Ángel
19 Macías-Díaz, Jorge Eduardo
19 Rossi, Julio Daniel
19 Shen, Wenxian
19 Velázquez, Juan J. L.
18 Aronson, Donald G.
18 Du, Yihong
18 Véron, Laurent
17 Hayashi, Nakao
17 Yin, Hongming
17 Zheng, Pan
16 Bao, Gang
16 Gao, Wenjie
16 Karatzas, Ioannis
16 Lions, Pierre-Louis
16 Yong, Jiongmin
16 Zaag, Hatem
15 Bertsch, Michiel
15 Bögelein, Verena
15 DiBenedetto, Emmanuele
15 Ding, Juntang
15 Escher, Joachim
15 Kamin, Shoshana
15 Kang, Hyeonbae
15 Mingione, Giuseppe
15 Rodríguez-Bernal, Aníbal
15 Taranets, Roman M.
15 Valdinoci, Enrico
15 Yin, Jingxue
14 Chechkin, Gregory Aleksandrovich
14 Ishige, Kazuhiro
14 Perthame, Benoît
14 Tello, José Ignacio
14 Weiss, Georg Sebastian
14 Wu, Junde
13 Amann, Herbert
13 Cheng, Jianfeng
13 Hao, Wenrui
13 Karakhanyan, Aram L.
13 Le, Dung
13 Lenhart, Suzanne M.
13 Prüß, Jan Wilhelm
13 Qi, Yuanwei
13 Salsa, Sandro
13 Suzuki, Takashi
13 Tarzia, Domingo Alberto
13 Tesei, Alberto
13 Zhang, Xicheng
12 Alessandrini, Giovanni
12 Ambrazevičius, Algirdas
12 Balachandran, Krishnan
12 Bandle, Catherine
12 Bellomo, Nicola
12 Fila, Marek
12 Guo, Boling
12 Kim, Kwang Ik
12 Lee, Ki-Ahm
12 Lesnic, Daniel
12 Pascucci, Andrea
12 Vasylyeva, Nataliya V.
12 Wang, Liangchen
12 Yang, Zhou
11 Barron, Emmanuel Nicholas
11 Beretta, Elena
11 Denisov, Vasiliĭ Nikolaevich
11 Elliott, Robert James
11 Fernández-Cara, Enrique
11 Fitzgibbon, William Edward
11 Gol’dman, Nataliya L’vovna
11 Hu, Guanghui
...and 7,767 more Authors
all top 5

Cited in 601 Serials

592 Journal of Mathematical Analysis and Applications
564 Journal of Differential Equations
242 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
234 Nonlinear Analysis. Theory, Methods & Applications
206 Archive for Rational Mechanics and Analysis
191 Transactions of the American Mathematical Society
144 Communications in Partial Differential Equations
119 Journal of Functional Analysis
110 Applicable Analysis
110 Applied Mathematics and Computation
106 Annali di Matematica Pura ed Applicata. Serie Quarta
102 Nonlinear Analysis. Real World Applications
93 Calculus of Variations and Partial Differential Equations
91 Journal of Computational and Applied Mathematics
91 Stochastic Processes and their Applications
89 Proceedings of the American Mathematical Society
85 Computers & Mathematics with Applications
84 Mathematical Methods in the Applied Sciences
82 Applied Mathematics and Optimization
81 Journal of Optimization Theory and Applications
72 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
71 Journal of Mathematical Sciences (New York)
70 ZAMP. Zeitschrift für angewandte Mathematik und Physik
68 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
66 Discrete and Continuous Dynamical Systems. Series B
61 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
61 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
59 Journal de Mathématiques Pures et Appliquées. Neuvième Série
59 SIAM Journal on Mathematical Analysis
58 Journal of Mathematical Biology
57 Mathematische Zeitschrift
55 Discrete and Continuous Dynamical Systems
51 Mathematische Annalen
50 Stochastic Analysis and Applications
49 Communications in Mathematical Physics
44 Applied Mathematics Letters
43 The Annals of Applied Probability
43 Boundary Value Problems
42 Bulletin of Mathematical Biology
39 Mathematics of Computation
39 Advances in Mathematics
39 Journal of Theoretical Biology
38 Probability Theory and Related Fields
38 European Journal of Applied Mathematics
37 Journal of Mathematical Physics
37 Numerische Mathematik
37 Mathematical and Computer Modelling
36 Stochastics
36 NoDEA. Nonlinear Differential Equations and Applications
35 Siberian Mathematical Journal
33 Journal d’Analyse Mathématique
33 Journal of Computational Physics
33 Manuscripta Mathematica
33 Journal of Dynamics and Differential Equations
32 Systems & Control Letters
32 Journal of Evolution Equations
31 Acta Applicandae Mathematicae
30 Mathematical Biosciences
29 Ukrainian Mathematical Journal
28 Israel Journal of Mathematics
28 Mathematical Notes
28 Communications on Pure and Applied Analysis
27 Computer Methods in Applied Mechanics and Engineering
27 Numerical Functional Analysis and Optimization
27 Bulletin of the American Mathematical Society
26 Automatica
26 Czechoslovak Mathematical Journal
26 Rendiconti del Seminario Matematico della Università di Padova
26 SIAM Journal on Control and Optimization
26 Physica D
25 The Annals of Probability
25 Journal of Economic Theory
25 Differential Equations
24 Publications of the Research Institute for Mathematical Sciences, Kyoto University
24 Quarterly of Applied Mathematics
24 Journal of Economic Dynamics & Control
24 Comptes Rendus. Mathématique. Académie des Sciences, Paris
23 Communications on Pure and Applied Mathematics
23 Zeitschrift für Analysis und ihre Anwendungen
23 Applied Numerical Mathematics
23 Acta Mathematicae Applicatae Sinica. English Series
22 Journal of Applied Mathematics and Mechanics
22 Rocky Mountain Journal of Mathematics
22 SIAM Journal on Applied Mathematics
22 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
21 International Journal of Control
21 Duke Mathematical Journal
21 Journal of Soviet Mathematics
21 Journal of Scientific Computing
21 The Journal of Geometric Analysis
21 Potential Analysis
21 Doklady Mathematics
20 Applied Mathematical Modelling
20 Acta Mathematica Sinica. English Series
20 Discrete and Continuous Dynamical Systems. Series S
20 Science China. Mathematics
19 Acta Mathematica
19 Advances in Difference Equations
19 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser
18 Chinese Annals of Mathematics. Series B
...and 501 more Serials
all top 5

Cited in 58 Fields

5,467 Partial differential equations (35-XX)
1,047 Probability theory and stochastic processes (60-XX)
970 Biology and other natural sciences (92-XX)
849 Fluid mechanics (76-XX)
773 Numerical analysis (65-XX)
745 Calculus of variations and optimal control; optimization (49-XX)
609 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
474 Systems theory; control (93-XX)
462 Ordinary differential equations (34-XX)
358 Operator theory (47-XX)
320 Mechanics of deformable solids (74-XX)
256 Classical thermodynamics, heat transfer (80-XX)
224 Integral equations (45-XX)
185 Dynamical systems and ergodic theory (37-XX)
167 Global analysis, analysis on manifolds (58-XX)
156 Functional analysis (46-XX)
147 Statistical mechanics, structure of matter (82-XX)
134 Optics, electromagnetic theory (78-XX)
130 Potential theory (31-XX)
128 Differential geometry (53-XX)
104 Operations research, mathematical programming (90-XX)
96 Statistics (62-XX)
66 Real functions (26-XX)
61 Quantum theory (81-XX)
41 Computer science (68-XX)
38 Harmonic analysis on Euclidean spaces (42-XX)
36 Information and communication theory, circuits (94-XX)
34 Measure and integration (28-XX)
34 Geophysics (86-XX)
32 Approximations and expansions (41-XX)
29 Difference and functional equations (39-XX)
25 Astronomy and astrophysics (85-XX)
24 Mechanics of particles and systems (70-XX)
23 Integral transforms, operational calculus (44-XX)
21 Functions of a complex variable (30-XX)
20 Relativity and gravitational theory (83-XX)
14 General and overarching topics; collections (00-XX)
13 Convex and discrete geometry (52-XX)
13 General topology (54-XX)
11 Several complex variables and analytic spaces (32-XX)
10 Special functions (33-XX)
8 History and biography (01-XX)
8 Topological groups, Lie groups (22-XX)
8 Manifolds and cell complexes (57-XX)
7 Linear and multilinear algebra; matrix theory (15-XX)
7 Nonassociative rings and algebras (17-XX)
7 Abstract harmonic analysis (43-XX)
6 Combinatorics (05-XX)
5 Number theory (11-XX)
5 Algebraic topology (55-XX)
4 Group theory and generalizations (20-XX)
3 Algebraic geometry (14-XX)
3 Geometry (51-XX)
3 Mathematics education (97-XX)
2 Mathematical logic and foundations (03-XX)
2 Associative rings and algebras (16-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Commutative algebra (13-XX)

Citations by Year

Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.