An inhomogeneous nonlocal diffusion problem with unbounded steps
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Date
2016
Journal Title
Journal ISSN
Volume Title
Publisher
SPRINGER BASEL AG
Abstract
We consider the following nonlocal equation
integral J (x-y/g(y)) u(y)/g(y) dy - u(x) = 0 x is an element of R,
where J is an even, compactly supported, Holder continuous kernel with unit integral and g is a continuous positive function. Our main concern will be with unbounded functions g, contrary to previous works. More precisely, we study the influence of the growth of g at infinity on the integrability of positive solutions of this equation, therefore determining the asymptotic behavior as t -> +infinity of the solutions to the associated evolution problem in terms of the growth of g.
integral J (x-y/g(y)) u(y)/g(y) dy - u(x) = 0 x is an element of R,
where J is an even, compactly supported, Holder continuous kernel with unit integral and g is a continuous positive function. Our main concern will be with unbounded functions g, contrary to previous works. More precisely, we study the influence of the growth of g at infinity on the integrability of positive solutions of this equation, therefore determining the asymptotic behavior as t -> +infinity of the solutions to the associated evolution problem in terms of the growth of g.
Description
Keywords
SPREADING SPEEDS, MONOSTABLE EQUATIONS, STATIONARY SOLUTIONS, ASYMPTOTIC-BEHAVIOR, TRAVELING-WAVES, EXISTENCE, UNIQUENESS, DISPERSAL, FRONTS, MODEL