Maximum principles and comparison theorems for semilinear parabolic systems and their applications

DOI10.1017/S0308210500029541zbMath0791.35006MaRDI QIDQ4277237

Gang Lu, Sleeman, Brian D.

Publication date: 18 July 1994

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

semilinear parabolic problemsFitzHugh-Nagumo modelFujita type systemsgeneral comparison theoremsparabolic systems with mixed type monotonicitysingle nerve axon

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Maximum principles in context of PDEs (35B50) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items

Traveling waves and spread rates for a West Nile virus model, Global existence and blow-up for a class of semilinear parabolic systems: A Cauchy Problem, Subsolutions and super solutions to systems of parabolic equations with applications to generalized Fujita‐type systems, Viscosity solutions of fully nonlinear parabolic systems., Optimal social distancing through cross-diffusion control for a disease outbreak PDE model, Global asymptotic behavior in a periodic competitor-competitor-mutualist parabolic system, The role of critical exponents in blow-up theorems: The sequel, On the stability of equilibria to weakly coupled parabolic systems in unbounded domains, On global existence for semilinear parabolic systems, Stable Equilibria to Parabolic Systems in Unbounded Domains, A maximum principle for semilinear parabolic systems and applications, Petrov-Galerkin methods for systems of nonlinear reaction-diffusion equations

Cites Work

• Unnamed Item
• Unnamed Item
• Quasimonotone systems and convergence to equilibrium in a population genetic model
• Comparison principles for reaction-diffusion systems: Irregular comparison functions and applications to questions of stability and speed of propagation of disturbances
• Geometric theory of semilinear parabolic equations
• Threshold phenomena for a reaction-diffusion system
• Boundedness and blow up for a semilinear reaction-diffusion system
• A Fujita type global existence-global nonexistence theorem for a weakly coupled system of reaction-diffusion equations
• Multidimensional nonlinear diffusion arising in population genetics
• THE APPLICATION OF A FIXED-POINT THEOREM TO A VARIETY OF NONLINEAR STABILITY PROBLEMS
• The Role of Critical Exponents in Blowup Theorems
• Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets
• Corrigendum