Publicación: Parabolic equations with natural growth approximated by nonlocal equations
Fecha
2021
Autores
Leonori, Tommaso
Molino, Alexis
Segura De León, Sergio
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info:eu-repo/semantics/openAccess
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World Scientific
Resumen
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.
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Categorías UNESCO
Palabras clave
nonlocal problems, KPZ equation, nonlinear parabolic equation, sasymptotic behavior of solutions
Citación
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
Centro
Facultad de Ciencias
Departamento
Matemáticas Fundamentales