Existence and stability of multidimensional travelling waves in the monostable case

DOI10.1007/BF02808184zbMath0929.35064OpenAlexW1986707225MaRDI QIDQ1293985

A. I. Volpert, Vitaly A. Volpert

Publication date: 1 December 1999

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02808184

zbMATH Keywords

stability conditionsquasilinear parabolic systems

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) Second-order parabolic systems (35K40)

Related Items (10)

Quenching of flames by fluid advection ⋮ Spatial decay and stability of traveling fronts for degenerate Fisher type equations in cylinder ⋮ Multidimensional stability of planar traveling waves for the delayed nonlocal dispersal competitive Lotka-Volterra system ⋮ Stability of planar traveling waves for a class of Lotka-Volterra competition systems with time delay and nonlocal reaction term ⋮ Existence of heteroclinic orbits for systems satisfying monotonicity conditions. ⋮ EXISTENCE OF MULTIDIMENSIONAL TRAVELLING WAVES AND SYSTEMS OF WAVES ⋮ Generalized travelling waves for perturbed monotone reaction-diffusion systems ⋮ Non-planar fronts in Boussinesq reactive flows ⋮ Quenching and propagation in KPP reaction-diffusion equations with a heat loss ⋮ MULTIDIMENSIONAL STABILITY OF PLANAR WAVES FOR DELAYED REACTION-DIFFUSION EQUATION WITH NONLOCAL DIFFUSION

Cites Work

• Existence of multidimensional travelling wave solutions of an initial boundary value problem
• Stability of travelling fronts in a model for flame propagation. I: Linear analysis
• On the stability of waves of nonlinear parabolic systems
• Topological degree for elliptic operators in unbounded cylinders
• Travelling fronts in cylinders
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Travelling wavefronts of reaction-diffusion equations in cylindrical domains
• A Parabolic Equation of the KPP Type in Higher Dimensions
• Generation of Analytic Semigroups by Strongly Elliptic Operators
• Analytic semigroups and optimal regularity in parabolic problems
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