×

zbMATH — the first resource for mathematics

Ludwig, Donald

Compute Distance To:
Author ID: ludwig.donald Recent zbMATH articles by "Ludwig, Donald"
Published as: Ludwig, D.; Ludwig, Donald
Documents Indexed: 41 Publications since 1959, including 2 Books

Publications by Year

Citations contained in zbMATH Open

30 Publications have been cited 568 times in 515 Documents Cited by Year
The Radon transform on Euclidean space. Zbl 0134.11305
Ludwig, Donald
92
1966
Spatial patterning of the spruce budworm. Zbl 0412.92020
Ludwig, D.; Aronson, D. G.; Weinberger, H. F.
76
1979
Uniform asymptotic expansions at a caustic. Zbl 0163.13703
Ludwig, Donald
66
1966
Persistence of dynamical systems under random perturbations. Zbl 0312.60040
Ludwig, Donald
54
1975
An inequality for the reduced wave operator and the justification of geometrical optics. Zbl 0157.18701
Morawetz, Cathleen S.; Ludwig, D.
41
1968
Exact and asymptotic solutions of the Cauchy problem. Zbl 0098.29601
Ludwig, Donald
38
1960
Final size distributions for epidemics. Zbl 0318.92025
Ludwig, Donald
33
1975
Uniform asymptotic expansion of the field scattered by a convex object at high frequencies. Zbl 0154.12802
Ludwig, Donald
29
1967
Propagation of singularities along characteristics with nonuniform multiplicity. Zbl 0159.39001
Ludwig, Donald; Granoff, Barry
19
1968
Uniform asymptotic theory of creeping waves. Zbl 0154.12103
Lewis, Robert M.; Bleistein, Norman; Ludwig, Donald
19
1967
Optimal harvesting of a randomly fluctuating resource. II: Numerical methods and results. Zbl 0445.93047
Ludwig, Donald; Varah, James M.
17
1979
Optimal harvesting of a randomly fluctuating resource. I: Application of perturbation methods. Zbl 0428.49024
Ludwig, Donald
13
1979
Conical refraction in crystal optics and hydromagnetics. Zbl 0112.21202
Ludwig, Donald
12
1961
Evolutionary stability of plant communities and the maintenance of multiple dispersal types. Zbl 0737.92022
Ludwig, Donald; Levin, Simon A.
10
1991
Probability of extinction in a stochastic competition. Zbl 0373.92024
Mangel, Marc; Ludwig, Donald
6
1977
Uniform asymptotic expansions for wave propagation and diffraction problems. Zbl 0202.38103
Ludwig, Donald
6
1970
The generalized Huyghens’ principle for reflecting bodies. Zbl 0167.10102
Morawetz, Cathleen S.; Ludwig, D.
6
1969
A singular perturbation problem in the theory of population extinction. Zbl 0351.92023
Ludwig, Donald
5
1976
Singularities of superpositions of distributions. Zbl 0143.20803
Ludwig, Donald
5
1965
Qualitative behavior of stochastic epidemics. Zbl 0318.92026
Ludwig, Donald
4
1975
The accuracy of the diffusion approximation to the expected time to extinction for some discrete stochastic processes. Zbl 0515.60084
Grasman, J.; Ludwig, D.
3
1983
Stochastic approximation for the general epidemic. Zbl 0272.92015
Ludwig, Donald
3
1973
Stochastic population theories. Notes by Michael Levandowsky. Corr. reprint of the 1st ed. Zbl 0409.92011
Ludwig, Donald
2
1978
Boundary layers in the field scattered by a convex object at high frequencies. Zbl 0187.03304
Ludwig, Donald
2
1969
Distributions as tools for the generalization of Riemann’s formula for hyperbolic differential equations. Zbl 0117.06302
Courant, Richard; Ludwig, D.
2
1959
An unusual free boundary problem from the theory of optimal harvesting. Zbl 0427.92016
Ludwig, Donald
1
1979
Approximate solutions for stochastic epidemics. Zbl 0336.92018
Ludwig, Donald
1
1975
Calculation of wave amplitudes by ray tracing. Zbl 0278.76032
Chen, Kenneth C.; Ludwig, Donald
1
1973
Tangential characteristics and coupling of waves. Zbl 0237.35052
Gautesen, A. K.; Ludwig, D.
1
1972
Wave propagation near a smooth caustic. Zbl 0142.37503
Ludwig, Donald
1
1965
Evolutionary stability of plant communities and the maintenance of multiple dispersal types. Zbl 0737.92022
Ludwig, Donald; Levin, Simon A.
10
1991
The accuracy of the diffusion approximation to the expected time to extinction for some discrete stochastic processes. Zbl 0515.60084
Grasman, J.; Ludwig, D.
3
1983
Spatial patterning of the spruce budworm. Zbl 0412.92020
Ludwig, D.; Aronson, D. G.; Weinberger, H. F.
76
1979
Optimal harvesting of a randomly fluctuating resource. II: Numerical methods and results. Zbl 0445.93047
Ludwig, Donald; Varah, James M.
17
1979
Optimal harvesting of a randomly fluctuating resource. I: Application of perturbation methods. Zbl 0428.49024
Ludwig, Donald
13
1979
An unusual free boundary problem from the theory of optimal harvesting. Zbl 0427.92016
Ludwig, Donald
1
1979
Stochastic population theories. Notes by Michael Levandowsky. Corr. reprint of the 1st ed. Zbl 0409.92011
Ludwig, Donald
2
1978
Probability of extinction in a stochastic competition. Zbl 0373.92024
Mangel, Marc; Ludwig, Donald
6
1977
A singular perturbation problem in the theory of population extinction. Zbl 0351.92023
Ludwig, Donald
5
1976
Persistence of dynamical systems under random perturbations. Zbl 0312.60040
Ludwig, Donald
54
1975
Final size distributions for epidemics. Zbl 0318.92025
Ludwig, Donald
33
1975
Qualitative behavior of stochastic epidemics. Zbl 0318.92026
Ludwig, Donald
4
1975
Approximate solutions for stochastic epidemics. Zbl 0336.92018
Ludwig, Donald
1
1975
Stochastic approximation for the general epidemic. Zbl 0272.92015
Ludwig, Donald
3
1973
Calculation of wave amplitudes by ray tracing. Zbl 0278.76032
Chen, Kenneth C.; Ludwig, Donald
1
1973
Tangential characteristics and coupling of waves. Zbl 0237.35052
Gautesen, A. K.; Ludwig, D.
1
1972
Uniform asymptotic expansions for wave propagation and diffraction problems. Zbl 0202.38103
Ludwig, Donald
6
1970
The generalized Huyghens’ principle for reflecting bodies. Zbl 0167.10102
Morawetz, Cathleen S.; Ludwig, D.
6
1969
Boundary layers in the field scattered by a convex object at high frequencies. Zbl 0187.03304
Ludwig, Donald
2
1969
An inequality for the reduced wave operator and the justification of geometrical optics. Zbl 0157.18701
Morawetz, Cathleen S.; Ludwig, D.
41
1968
Propagation of singularities along characteristics with nonuniform multiplicity. Zbl 0159.39001
Ludwig, Donald; Granoff, Barry
19
1968
Uniform asymptotic expansion of the field scattered by a convex object at high frequencies. Zbl 0154.12802
Ludwig, Donald
29
1967
Uniform asymptotic theory of creeping waves. Zbl 0154.12103
Lewis, Robert M.; Bleistein, Norman; Ludwig, Donald
19
1967
The Radon transform on Euclidean space. Zbl 0134.11305
Ludwig, Donald
92
1966
Uniform asymptotic expansions at a caustic. Zbl 0163.13703
Ludwig, Donald
66
1966
Singularities of superpositions of distributions. Zbl 0143.20803
Ludwig, Donald
5
1965
Wave propagation near a smooth caustic. Zbl 0142.37503
Ludwig, Donald
1
1965
Conical refraction in crystal optics and hydromagnetics. Zbl 0112.21202
Ludwig, Donald
12
1961
Exact and asymptotic solutions of the Cauchy problem. Zbl 0098.29601
Ludwig, Donald
38
1960
Distributions as tools for the generalization of Riemann’s formula for hyperbolic differential equations. Zbl 0117.06302
Courant, Richard; Ludwig, D.
2
1959
all top 5

Cited by 643 Authors

9 Cosner, Chris
9 Spence, Euan A.
8 Hanson, Floyd B.
8 Liu, Meng
7 Ball, Frank G.
7 Cantrell, Robert Stephen
6 Babich, Vasiliĭ Mikhaĭlovich
6 Bai, Chuanzhi
6 Graham, Ivan G.
6 Ludwig, Donald
6 Quinto, Eric Todd
5 Dineva, Petia S.
5 Nguyen, Hoai-Minh
5 Pellis, Lorenzo
5 Savina, Tatiana V.
4 Estrada, Ricardo
4 Grigor’eva, N. S.
4 Hamada, Yûsaku
4 Lan, Kunquan
4 Louis, Alfred Karl
4 Manolis, George D.
4 Qian, Jianliang
4 Qu, Gangrong
4 Rangelov, Tsviatko V.
4 Ryan, Dennis
4 Sadiq, Kamran
4 Shivaji, Ratnasingham
4 Smyshlyaev, Valery P.
4 Tamasan, Alexandru
4 Trapman, Pieter
4 Yeh, Tzung-Shin
4 Zauderer, Erich
3 Alber, Hans-Dieter
3 Barclay, D. W.
3 Bloom, Clifford O.
3 Borovikov, Vladimir A.
3 Burridge, Robert R.
3 Day, Martin V.
3 Gårding, Lars
3 Gautesen, Arthur K.
3 Grasman, Johan
3 Guo, Ben-Yu
3 Helgason, Sigurdur
3 Hertle, Alexander
3 Keller, Joseph Bishop
3 Lafitte, Olivier D.
3 Lefèvre, Claude
3 Lewis, Robert Michael
3 Li, Yao
3 Lin, Wei
3 Lutscher, Frithjof
3 Manoranjan, Valipuram S.
3 Moodie, T. Bryant
3 Nakamura, Gen
3 Natterer, Frank
3 Neal, Peter J.
3 Picard, Philippe
3 Ramm, Alexander G.
3 Rubin, Boris
3 Rubtsov, Yu. K.
3 Runborg, Olof
3 Solmon, Donald C.
3 Taylor, Michael Eugene
3 Tier, Charles
3 Turelli, Michael
3 Vogelius, Michael S.
3 Ward, Michael J.
3 Yakhno, Valery Georgievich
3 Yamada, Yoshio
3 Yi, Yingfei
2 Allen, Linda J. S.
2 Apaloo, Joseph
2 Bazer, Jack
2 Benamou, Jean-David
2 Berestycki, Henri
2 Bleistein, Norman
2 Chandler-Wilde, Simon N.
2 Costa, David Goldstein
2 De Micheli, Enrico
2 Eckhoff, Knut S.
2 Ellner, Stephen P.
2 Eskin, Gregory
2 Ferguson, Neil M.
2 Fraser, Christophe
2 Freedman, Herbert Irving
2 Ganesh, Madhu
2 Gard, Thomas C.
2 Gonzalez, Fulton B.
2 Goodhue, William L.
2 Gordillo, Luis F.
2 Gosse, Laurent
2 Hermans, Aad J.
2 Hethcote, Herbert W.
2 House, Thomas
2 Jiang, Ming
2 Kaneko, Yuki
2 Kirpichnikova, N. Ya.
2 Krisztin, Tibor
2 Kucherenko, Valeri V.
2 Kurusa, Árpád
...and 543 more Authors
all top 5

Cited in 157 Serials

36 Mathematical Biosciences
35 Journal of Mathematical Biology
29 Journal of Mathematical Analysis and Applications
27 Wave Motion
19 Bulletin of Mathematical Biology
18 Journal of Soviet Mathematics
17 Communications in Partial Differential Equations
15 Theoretical Population Biology
13 Journal of Differential Equations
10 Communications on Pure and Applied Mathematics
9 Transactions of the American Mathematical Society
7 Journal of Computational Physics
7 Mathematical Methods in the Applied Sciences
7 Journal of Computational and Applied Mathematics
7 Numerische Mathematik
7 Journal of Theoretical Biology
6 Archive for Rational Mechanics and Analysis
6 Journal of Statistical Physics
6 Applied Mathematics and Computation
6 Publications of the Research Institute for Mathematical Sciences, Kyoto University
6 Bulletin of the American Mathematical Society
5 Acta Mechanica
5 Advances in Mathematics
5 SIAM Journal on Mathematical Analysis
4 Mathematical Notes
4 Mathematics of Computation
4 Annali di Matematica Pura ed Applicata. Serie Quarta
4 Duke Mathematical Journal
4 Mathematische Zeitschrift
4 Acta Mathematicae Applicatae Sinica. English Series
4 Applied Mathematics Letters
4 Russian Journal of Mathematical Physics
4 Engineering Analysis with Boundary Elements
3 Applicable Analysis
3 Journal of Applied Mathematics and Mechanics
3 Journal of Engineering Mathematics
3 Journal of Fluid Mechanics
3 Rocky Mountain Journal of Mathematics
3 Annales de l’Institut Fourier
3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
3 Journal of Functional Analysis
3 Studies in Applied Mathematics
3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
3 Natural Resource Modeling
3 Journal of Biological Dynamics
2 Computers & Mathematics with Applications
2 Inverse Problems
2 Soviet Applied Mechanics
2 Acta Mathematica
2 Journal of Applied Probability
2 Mathematische Annalen
2 Proceedings of the American Mathematical Society
2 Proceedings of the Japan Academy. Series A
2 American Journal of Mathematical and Management Sciences
2 Journal de Mathématiques Pures et Appliquées. Neuvième Série
2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
2 Bulletin of the American Mathematical Society. New Series
2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
2 Communications in Numerical Methods in Engineering
2 Journal of Mathematical Sciences (New York)
2 Chaos
2 Discrete and Continuous Dynamical Systems. Series B
2 Communications on Pure and Applied Analysis
2 Central European Journal of Mathematics
2 Advances in Difference Equations
2 Mathematical Biosciences and Engineering
2 Analysis and Mathematical Physics
2 Nonlinear Analysis. Theory, Methods & Applications
1 Artificial Intelligence
1 Bulletin of the Australian Mathematical Society
1 Communications in Mathematical Physics
1 Computer Methods in Applied Mechanics and Engineering
1 International Journal of Engineering Science
1 International Journal of Systems Science
1 Journal d’Analyse Mathématique
1 Journal of Mathematical Physics
1 Stochastics
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Arkiv för Matematik
1 Reviews in Mathematical Physics
1 Prikladnaya Matematika i Mekhanika
1 Acta Mathematica Vietnamica
1 Applied Mathematics and Optimization
1 BIT
1 Bulletin de la Société Mathématique de France
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of Statistical Planning and Inference
1 Kodai Mathematical Journal
1 Manuscripta Mathematica
1 Mathematics and Computers in Simulation
1 Monatshefte für Mathematik
1 Numerical Functional Analysis and Optimization
1 RAIRO. Analyse Numérique
1 Rendiconti del Circolo Matemàtico di Palermo. Serie II
1 SIAM Journal on Numerical Analysis
1 Siberian Mathematical Journal
1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
1 Optimal Control Applications & Methods
1 Statistics & Probability Letters
1 Stochastic Analysis and Applications
...and 57 more Serials
all top 5

Cited in 44 Fields

215 Partial differential equations (35-XX)
179 Biology and other natural sciences (92-XX)
84 Probability theory and stochastic processes (60-XX)
74 Numerical analysis (65-XX)
62 Integral transforms, operational calculus (44-XX)
38 Fluid mechanics (76-XX)
38 Optics, electromagnetic theory (78-XX)
33 Mechanics of deformable solids (74-XX)
31 Ordinary differential equations (34-XX)
23 Integral equations (45-XX)
18 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
17 Systems theory; control (93-XX)
16 Global analysis, analysis on manifolds (58-XX)
15 Functional analysis (46-XX)
13 Operator theory (47-XX)
12 Dynamical systems and ergodic theory (37-XX)
10 Abstract harmonic analysis (43-XX)
9 Harmonic analysis on Euclidean spaces (42-XX)
9 Differential geometry (53-XX)
9 Statistical mechanics, structure of matter (82-XX)
9 Operations research, mathematical programming (90-XX)
8 Calculus of variations and optimal control; optimization (49-XX)
7 Statistics (62-XX)
6 Potential theory (31-XX)
6 Mechanics of particles and systems (70-XX)
6 Quantum theory (81-XX)
5 Combinatorics (05-XX)
5 Difference and functional equations (39-XX)
4 Functions of a complex variable (30-XX)
4 Several complex variables and analytic spaces (32-XX)
3 Real functions (26-XX)
3 Special functions (33-XX)
3 Approximations and expansions (41-XX)
3 Information and communication theory, circuits (94-XX)
2 Topological groups, Lie groups (22-XX)
2 Geophysics (86-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Linear and multilinear algebra; matrix theory (15-XX)
1 Measure and integration (28-XX)
1 Manifolds and cell complexes (57-XX)
1 Computer science (68-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Relativity and gravitational theory (83-XX)

Citations by Year