Transition fronts for periodic bistable reaction-diffusion equations
نویسندگان
چکیده
منابع مشابه
Transition fronts for periodic bistable reaction-diffusion equations
This paper is concerned with the existence and qualitative properties of transition fronts for spatially periodic reaction-diffusion equations with bistable nonlinearities. The notion of transition fronts connecting two stable steady states generalizes the standard notion of pulsating fronts. In this paper, we prove that the time-global solutions in the class of transition fronts share some com...
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We use a new method in the study of Fisher-KPP reaction-diffusion equations to prove existence of transition fronts for inhomogeneous KPP-type non-linearities in one spatial dimension. We also obtain new estimates on entire solutions of some KPP reactiondiffusion equations in several spatial dimensions. Our method is based on the construction of suband super-solutions to the non-linear PDE from...
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We consider the semilinear parabolic equation ut = uxx + f(u), x ∈ R, t > 0, (A) where f is a bistable nonlinearity. It is well-known that for a large class of initial data, the corresponding solutions converge to traveling fronts. We give a new proof of this classical result as well as some generalizations. Our proof uses a geometric method, which makes use of spatial trajectories {(u(x, t), u...
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This paper is chiefly concerned with qualitative properties of some reaction-diffusion fronts. The recently defined notions of transition fronts generalize the standard notions of traveling fronts. In this paper, we show the existence and the uniqueness of the global mean speed of bistable transition fronts in RN . This speed is proved to be independent of the shape of the level sets of the fro...
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ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2015
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-015-0874-6