Publication: Parabolic equations with natural growth approximated by nonlocal equations
Loading...
Date
2021
Editor
Director
Advisor
Coordinator
Commentator
Reviewer
Illustrator
Access rights
info:eu-repo/semantics/openAccess
Journal Title
Journal ISSN
Volume Title
Publisher
World Scientific
Abstract
In this paper, we study several aspects related with solutions of nonlocal problems whose prototype is
{u(t) = integral N-R J (x - y)(u(y, t) u( x, t))g (u(y , t) u( x, t))dy in Omega x (0, T),
u(x, 0) = u(0)(x) in Omega,
where we take, as the most important instance, g(s) similar to 1 + mu/2 s/1+mu(2)s(2) with mu is an element of R as well as mu(0)is an element of L-1 (Omega), J is a smooth symmetric function with compact support and S2 is either a bounded smooth subset of R-N, with nonlocal Dirichlet boundary condition, or RN itself. The results deal with existence, uniqueness, comparison principle and asymptotic behavior. Moreover, we prove that if the kernel is resealed in a suitable way, the unique solution of the above problem converges to a solution of the deterministic Kardar Parisi Zhang equation.
Description
UNESCO Categories
Keywords
nonlocal problems, KPZ equation, nonlinear parabolic equation, sasymptotic behavior of solutions
Citation
Leonori, T., Molino, A., Segura De León, S. ; Parabolic equations with natural growth approximated by nonlocal equations (2021) Communications in Contemporary Mathematics, 23 (1), art. no. 1950088. : http://doi.org/10.1142/S0219199719500883
Center
Facultad de Ciencias
Department
Matemáticas Fundamentales