Discrete and Continuous Dynamical Systems · 2017 · 26 citations · 13 references
Banach SpacesEngineeringVariational AnalysisPde-constrained OptimizationSemi-implicit MethodParabolic EquationWeak TopologyNonlinear EquationFunctional AnalysisNonlinear Hyperbolic ProblemApproximation TheoryContinuation PrincipleCalculus Of VariationYosida ApproximationsApproximation Solvability MethodNonlinear Functional Analysis
A new approximation solvability method is developed for the study of semilinear differential equations with nonlocal conditions without the compactness of the semigroup and of the nonlinearity. The method is based on the Yosida approximations of the generator of C0-semigroup, the continuation principle, and the weak topology. It is shown how the abstract result can be applied to study the reaction-diffusion models.
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The non-local Fisher–KPP equation: travelling waves and steady states
Henri Berestycki, Grégoire Nadin, Benoı̂t Perthame et al. · Nonlinearity · 2009 · 286 citations