Leonori, TommasoMolino, AlexisSegura De León, Sergio2024-11-202024-11-202021Leonori, 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/S02191997195008830219-1997; e-ISSN: 1793-6683https://doi.org/10.1142/S0219199719500883https://hdl.handle.net/20.500.14468/24435In 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.eninfo:eu-repo/semantics/openAccess12 MatemáticasartículoNonlocal problemsKPZ equationnonlinear parabolic equationsasymptotic behavior of solutions