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## Rothe, Franz

Compute Distance To:
 Author ID: rothe.franz Published as: Rothe, F.; Rothe, Franz
 Documents Indexed: 32 Publications since 1974, including 1 Book
all top 5

#### Co-Authors

 23 single-authored 3 de Mottoni, Piero 3 Hadeler, Karl-Peter 2 Shafer, Douglas S. 1 an der Heiden, Uwe 1 Avrin, Joel D. 1 Vogt, Harald
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#### Serials

 4 Journal of Mathematical Biology 3 Mathematical Methods in the Applied Sciences 2 Applicable Analysis 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Nonlinear Analysis. Theory, Methods & Applications 1 Rocky Mountain Journal of Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal of Differential Equations 1 Journal für die Reine und Angewandte Mathematik 1 Manuscripta Mathematica 1 Studies in Applied Mathematics 1 Aequationes Mathematicae 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Bollettino della Unione Matemàtica Italiana. Serie VII. B 1 Nieuw Archief voor Wiskunde. Vijfde Serie 1 Lecture Notes in Mathematics
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#### Fields

 19 Partial differential equations (35-XX) 11 Biology and other natural sciences (92-XX) 7 Ordinary differential equations (34-XX) 6 Dynamical systems and ergodic theory (37-XX) 2 Algebraic topology (55-XX) 2 Probability theory and stochastic processes (60-XX) 2 Mechanics of particles and systems (70-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Numerical analysis (65-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX)

#### Citations contained in zbMATH Open

28 Publications have been cited 549 times in 482 Documents Cited by Year
Global solutions of reaction-diffusion systems. Zbl 0546.35003
Rothe, Franz
1984
Travelling fronts in nonlinear diffusion equations. Zbl 0343.92009
1975
Convergence to homogeneous equilibrium state for generalized Volterra- Lotka systems with diffusion. Zbl 0425.35055
De Mottoni, P.; Rothe, F.
1979
Convergence to the equilibrium state in the Volterra-Lotka diffusion equations. Zbl 0355.92013
Rothe, F.
1976
The periods of the Volterra-Lotka system. Zbl 0547.92011
Rothe, Franz
1985
Convergence to pushed fronts. Zbl 0516.35013
Rothe, Franz
1981
Convergence to travelling fronts in semilinear parabolic equations. Zbl 0389.35024
Rothe, Franz
1978
Uniform bounds from bounded $$L_ p-$$functionals in reaction-diffusion equations. Zbl 0457.35043
Rothe, F.
1982
Global existence of branches of stationary solutions for a system of reaction diffusion equations from biology. Zbl 0471.35031
Rothe, Franz
1981
Remarks on periods of planar Hamiltonian systems. Zbl 0769.34032
Rothe, Franz
1993
Stationary solutions of reaction-diffusion equations. Zbl 0424.35047
Hadeler, K. P.; Rothe, F.; Vogt, H.
1979
Nonhomogeneous spatial distributions of populations. Zbl 0315.92012
Hadeler, K. P.; an der Heiden, Uwe; Rothe, F.
1974
Multiple bifurcation in a predator-prey system with non-monotonic predator response. Zbl 0763.92011
Rothe, Franz; Shafer, Douglas S.
1992
Some analytical results about a simple reaction-diffusion system for morphogenesis. Zbl 0399.35091
Rothe, Franz
1979
Thermodynamics, real and complex periods of the Volterra model. Zbl 0591.92017
Rothe, Franz
1985
A singular perturbation analysis for a reaction-diffusion system describing pattern formation. Zbl 0452.35058
de Mottoni, P.; Rothe, F.
1980
A simple system of reaction-diffusion equations describing morphogenesis: Asymptotic behavior. Zbl 0425.35017
Rothe, F.; De Mottoni, P.
1979
Boundedness and decay estimates for a class of reaction-diffusion systems on $$\mathbb{R}^ n$$. Zbl 0815.35042
Avrin, Joel D.; Rothe, Franz
1994
A priori estimates for nonlinear Poisson equations and phase plane analysis of the Emden-Fowler equation. Zbl 0794.35058
Rothe, F.
1992
Asymptotic behavior of a nonhomogeneous predator-prey system with one diffusing and one sedentary species. Zbl 0513.92019
Rothe, F.
1983
Solutions for systems of nonlinear elliptic equations with nonlinear boundary conditions. Zbl 0414.35008
Rothe, F.
1979
A variant of Frobenius’ method for the Emden-Fowler equation. Zbl 0886.34006
Rothe, F.
1997
Hidden symmetry and bifurcation analysis of the Emden-Fowler equation. Zbl 0791.34031
Rothe, F.
1993
A priori estimates for reaction-diffusion systems. Zbl 0664.35050
Rothe, Franz
1988
An analogue to the Smale-Birkhoff homoclinic theorem for iterated entire mappings. Zbl 0809.58033
Rothe, Franz
1994
The bootstrap and feedback method for the nonlinear Poisson equation. Zbl 0817.35028
Rothe, F.
1994
Snapback repellers and semiconjugacy for iterated entire mappings. Global aspects of an old theorem of Poincaré. Zbl 0760.30009
Rothe, F.
1992
The energy-period function and perturbations of Hamiltonian systems in the plane. Zbl 0648.34049
Rothe, Franz
1987
A variant of Frobenius’ method for the Emden-Fowler equation. Zbl 0886.34006
Rothe, F.
1997
Boundedness and decay estimates for a class of reaction-diffusion systems on $$\mathbb{R}^ n$$. Zbl 0815.35042
Avrin, Joel D.; Rothe, Franz
1994
An analogue to the Smale-Birkhoff homoclinic theorem for iterated entire mappings. Zbl 0809.58033
Rothe, Franz
1994
The bootstrap and feedback method for the nonlinear Poisson equation. Zbl 0817.35028
Rothe, F.
1994
Remarks on periods of planar Hamiltonian systems. Zbl 0769.34032
Rothe, Franz
1993
Hidden symmetry and bifurcation analysis of the Emden-Fowler equation. Zbl 0791.34031
Rothe, F.
1993
Multiple bifurcation in a predator-prey system with non-monotonic predator response. Zbl 0763.92011
Rothe, Franz; Shafer, Douglas S.
1992
A priori estimates for nonlinear Poisson equations and phase plane analysis of the Emden-Fowler equation. Zbl 0794.35058
Rothe, F.
1992
Snapback repellers and semiconjugacy for iterated entire mappings. Global aspects of an old theorem of Poincaré. Zbl 0760.30009
Rothe, F.
1992
A priori estimates for reaction-diffusion systems. Zbl 0664.35050
Rothe, Franz
1988
The energy-period function and perturbations of Hamiltonian systems in the plane. Zbl 0648.34049
Rothe, Franz
1987
The periods of the Volterra-Lotka system. Zbl 0547.92011
Rothe, Franz
1985
Thermodynamics, real and complex periods of the Volterra model. Zbl 0591.92017
Rothe, Franz
1985
Global solutions of reaction-diffusion systems. Zbl 0546.35003
Rothe, Franz
1984
Asymptotic behavior of a nonhomogeneous predator-prey system with one diffusing and one sedentary species. Zbl 0513.92019
Rothe, F.
1983
Uniform bounds from bounded $$L_ p-$$functionals in reaction-diffusion equations. Zbl 0457.35043
Rothe, F.
1982
Convergence to pushed fronts. Zbl 0516.35013
Rothe, Franz
1981
Global existence of branches of stationary solutions for a system of reaction diffusion equations from biology. Zbl 0471.35031
Rothe, Franz
1981
A singular perturbation analysis for a reaction-diffusion system describing pattern formation. Zbl 0452.35058
de Mottoni, P.; Rothe, F.
1980
Convergence to homogeneous equilibrium state for generalized Volterra- Lotka systems with diffusion. Zbl 0425.35055
De Mottoni, P.; Rothe, F.
1979
Stationary solutions of reaction-diffusion equations. Zbl 0424.35047
Hadeler, K. P.; Rothe, F.; Vogt, H.
1979
Some analytical results about a simple reaction-diffusion system for morphogenesis. Zbl 0399.35091
Rothe, Franz
1979
A simple system of reaction-diffusion equations describing morphogenesis: Asymptotic behavior. Zbl 0425.35017
Rothe, F.; De Mottoni, P.
1979
Solutions for systems of nonlinear elliptic equations with nonlinear boundary conditions. Zbl 0414.35008
Rothe, F.
1979
Convergence to travelling fronts in semilinear parabolic equations. Zbl 0389.35024
Rothe, Franz
1978
Convergence to the equilibrium state in the Volterra-Lotka diffusion equations. Zbl 0355.92013
Rothe, F.
1976
Travelling fronts in nonlinear diffusion equations. Zbl 0343.92009
1975
Nonhomogeneous spatial distributions of populations. Zbl 0315.92012
Hadeler, K. P.; an der Heiden, Uwe; Rothe, F.
1974
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#### Cited by 659 Authors

 13 Rothe, Franz 11 Hamel, François 10 Fellner, Klemens 10 Marciniak-Czochra, Anna K. 9 Morgan, Jeff J. 8 Tang, Bao Quoc 8 Villadelprat, Jordi 7 Fitzgibbon, William Edward 6 Gasull, Armengol 6 Pierre, Michel 6 Shi, Junping 6 Suzuki, Takashi 6 Takagi, Izumi 5 Berestycki, Henri 5 Cao, Jinde 5 Desvillettes, Laurent 5 Li, Lige 5 Shukla, Jang Bahadur 5 Song, Qiankun 5 Volpert, Vitaly A. 5 Wang, Mingxin 4 Abdelmalek, Salem 4 Bendoukha, Samir 4 Bothe, Dieter 4 de Mottoni, Piero 4 Diekmann, Odo 4 Du, Yihong 4 Hadeler, Karl-Peter 4 Karch, Grzegorz 4 King, John Robert 4 Kirane, Mokhtar 4 Laamri, El Haj 4 Latos, Evangelos Antonios 4 Morgan, Jeffery J. 4 Ou, Chunhua 4 Roques, Lionel J. 4 Suzuki, Kanako 4 Temam, Roger Meyer 4 Waggoner, S. J. 4 Wei, Junjie 4 Zhao, Yulin 3 Balachandran, Krishnan 3 Brown, Kenneth J. 3 Escher, Joachim 3 Giletti, Thomas 3 Gnanavel, Soundararajan 3 Jung, Changyeol 3 Kimmel, Marek 3 Kishimoto, Kazuo 3 Kouachi, Said 3 Li, Wan-Tong 3 Lu, Junguo 3 Mañosas, Francesc 3 Nadirashvili, Nikolai S. 3 Ni, Wei-Ming 3 O’Dea, Reuben D. 3 Parshad, Rana D. 3 Rolland, Guillaume 3 Ruan, Shigui 3 Sabatini, Marco 3 Scheel, Arnd 3 Sherratt, Jonathan A. 3 Sun, Jianhua 3 Takeuchi, Yasuhiro 3 Trofimchuk, Sergei I. 3 Wan, Li 3 Wang, Jinfeng 3 Wang, Zhi Cheng 3 Yamada, Yoshio 3 Yi, Fengqi 3 Yin, Zhaoyang 3 Zanolin, Fabio 2 Ahn, Inkyung 2 Alaa, Noureddine 2 Alhasanat, Ahmad 2 Badraoui, Salah 2 Beauregard, Matthew A. 2 Benguria, Rafael D. 2 Bobrowski, Adam 2 Bonnefon, Olivier 2 Celiński, Rafał 2 Chen, Hongwei 2 Chen, Lansun 2 Chen, Shaohua 2 Chicone, Carmen C. 2 Chow, Pao-Liu 2 Cosner, Chris 2 Depassier, M. Cristina 2 dos Reis, Gonçalo 2 Ducrot, Arnaud 2 Engler, Hans 2 Fife, Paul C. 2 Fila, Marek 2 Franchi, Bruno 2 Gao, Peng 2 Garnier, Jimmy 2 Härting, Steffen 2 Hilhorst, Danielle 2 Hillen, Thomas 2 Hollis, Selwyn L. ...and 559 more Authors
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#### Cited in 121 Serials

 53 Journal of Differential Equations 38 Journal of Mathematical Analysis and Applications 24 Journal of Mathematical Biology 24 Nonlinear Analysis. Theory, Methods & Applications 22 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 13 Journal of Dynamics and Differential Equations 12 Mathematical Biosciences 12 Nonlinear Analysis. Real World Applications 11 Mathematical Methods in the Applied Sciences 10 Computers & Mathematics with Applications 10 Bulletin of Mathematical Biology 10 Discrete and Continuous Dynamical Systems. Series B 9 Chaos, Solitons and Fractals 9 SIAM Journal on Mathematical Analysis 8 Applicable Analysis 8 Applied Mathematics Letters 8 Communications in Partial Differential Equations 7 Proceedings of the American Mathematical Society 7 Physica D 7 Discrete and Continuous Dynamical Systems 6 Applied Mathematics and Computation 6 Theoretical Population Biology 5 Archive for Rational Mechanics and Analysis 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Transactions of the American Mathematical Society 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Japan Journal of Industrial and Applied Mathematics 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Discrete and Continuous Dynamical Systems. Series S 3 Communications in Mathematical Physics 3 Communications on Pure and Applied Mathematics 3 Rocky Mountain Journal of Mathematics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Zeitschrift für Analysis und ihre Anwendungen 3 Acta Mathematicae Applicatae Sinica. English Series 3 The Annals of Applied Probability 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Journal of Evolution Equations 3 Mediterranean Journal of Mathematics 3 Journal of Theoretical Biology 2 Journal of the Franklin Institute 2 Journal of Statistical Physics 2 Nonlinearity 2 Results in Mathematics 2 Siberian Mathematical Journal 2 Studies in Applied Mathematics 2 Applied Mathematics and Mechanics. (English Edition) 2 Acta Applicandae Mathematicae 2 Applied Mathematical Modelling 2 Journal of Nonlinear Science 2 Annales Mathématiques Blaise Pascal 2 NoDEA. Nonlinear Differential Equations and Applications 2 Bulletin des Sciences Mathématiques 2 Journal of Mathematical Chemistry 2 Journal of Biological Dynamics 1 Journal of Computational Physics 1 Journal of Engineering Mathematics 1 Lithuanian Mathematical Journal 1 Wave Motion 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Applied Mathematics and Optimization 1 Calcolo 1 Czechoslovak Mathematical Journal 1 Indiana University Mathematics Journal 1 Inventiones Mathematicae 1 Journal of Computational and Applied Mathematics 1 Journal of Optimization Theory and Applications 1 Mathematics and Computers in Simulation 1 Mathematische Zeitschrift 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Tohoku Mathematical Journal. Second Series 1 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Chinese Annals of Mathematics. Series B 1 Probability Theory and Related Fields 1 Revista Matemática Iberoamericana 1 Journal of the American Mathematical Society 1 Mathematical and Computer Modelling 1 European Journal of Applied Mathematics 1 Aequationes Mathematicae 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Potential Analysis 1 Advances in Computational Mathematics 1 Complexity 1 Journal of Difference Equations and Applications 1 Computing and Visualization in Science 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Chaos 1 Fractional Calculus & Applied Analysis 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Discrete Dynamics in Nature and Society 1 Communications in Nonlinear Science and Numerical Simulation 1 Qualitative Theory of Dynamical Systems 1 Journal of Nonlinear Mathematical Physics 1 Dynamical Systems 1 Advanced Nonlinear Studies ...and 21 more Serials
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#### Cited in 35 Fields

 387 Partial differential equations (35-XX) 207 Biology and other natural sciences (92-XX) 89 Ordinary differential equations (34-XX) 39 Dynamical systems and ergodic theory (37-XX) 22 Numerical analysis (65-XX) 20 Probability theory and stochastic processes (60-XX) 14 Operator theory (47-XX) 13 Classical thermodynamics, heat transfer (80-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 10 Integral equations (45-XX) 10 Systems theory; control (93-XX) 9 Statistical mechanics, structure of matter (82-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 Mechanics of particles and systems (70-XX) 6 Fluid mechanics (76-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Real functions (26-XX) 3 Difference and functional equations (39-XX) 3 Algebraic topology (55-XX) 2 History and biography (01-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 Computer science (68-XX) 2 Mechanics of deformable solids (74-XX) 2 Optics, electromagnetic theory (78-XX) 2 Operations research, mathematical programming (90-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Statistics (62-XX) 1 Quantum theory (81-XX) 1 Information and communication theory, circuits (94-XX)