Transition fronts for the Fisher-KPP equation
نویسندگان
چکیده
منابع مشابه
Multidimensional Transition Fronts for Fisher-kpp Reactions
We study entire solutions to homogeneous reactiondiffusion equations in several dimensions with Fisher-KPP reactions. Any entire solution 0 < u < 1 is known to satisfy lim t→−∞ sup ∣x∣≤c∣t∣ u(t, x) = 0 for each c < 2 √ f ′(0) , and we consider here those satisfying lim t→−∞ sup ∣x∣≤c∣t∣ u(t, x) = 0 for some c > 2 √ f ′(0) . When f is C and concave, our main result provides an almost complete ch...
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We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-front-type global in time solutions while creating a global in time bump-like solution. This is the first example of a medium in which no reaction-diffusion transition front exists. A weaker localized...
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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 study the one-dimensional Fisher-KPP equation, with an initial condition u0(x) that coincides with the step function except on a compact set. A well-known result of M. Bramson in [3, 4] states that, as t → +∞, the solution converges to a traveling wave located at the position X(t) = 2t − (3/2) log t + x0 + o(1), with the shift x0 that depends on u0. U. Ebert and W. Van Saarloos have formally...
متن کاملExponential Stability of the Traveling Fronts for a Pseudo-parabolic Fisher-kpp Equation
In this talk, I will introduce the stability of traveling front solutions for a pseudoparabolic Fisher-KPP equation. By applying geometric singular perturbation method, special Evans function estimates, detailed spectral analysis and C0 semigroup theories, all the traveling front solutions with non-critical speeds are proved to be locally exponentially stable in some appropriate exponentially w...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2016
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6609