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Strong solutions for stochastic nonlinear nonlocal parabolic equations
(2010)
In this article we investigate the existence and uniqueness of strong solutions to the initial-boundary value problem with homogeneous boundary conditions for a stochastic nonlinear parabolic equation of nonlocal type with ...
Higher-order boundary regularity estimates for nonlocal parabolic equations
(Springer, 2018-10)
We establish sharp higher-order Hölder regularity estimates up to the boundary for solutions to equations of the form ∂tu- Lu= f(t, x) in I× Ω where I⊂ R, Ω ⊂ Rn and f is Hölder continuous. The nonlocal operators L that ...
Some results for nonlocal elliptic and parabolic nonlinear equatións
(2017)
This thesis is devoted to the study of qualitative properties of degenerate elliptic equations where the diffusion is purely nonlocal, and it is carried out in the framework of the theory of viscosity solutions.
Nonlocal heat equations in the Heisenberg group
(Springer, 2017-10)
We study the following nonlocal diffusion equation in the Heisenberg group Hn,ut(z,s,t)=J∗u(z,s,t)-u(z,s,t),where ∗ denote convolution product and J satisfies appropriated hypothesis. For the Cauchy problem we obtain that ...
On abstract differential equations with nonlocal conditions involving the temporal derivative of the solution
(ELSEVIER SCIENCE BVAMSTERDAM, 2012)
In this paper we discuss the existence of solutions for a class of abstract differential equations with nonlocal conditions for which the nonlocal term involves the temporal derivative of the solution. Some concrete ...
Existencia y unicidad de soluciones para un problema de difusión no local reescalado
(Bogotá - Ciencias - Maestría en Ciencias - MatemáticasDepartamento de MatemáticasUniversidad Nacional de Colombia - Sede Bogotá, 2020-06-02)
We study a nonlocal difusion problem with the aim to decide on existence and uniqueness of solutions, and if that solutions satisfy some comparison principle.
Dinâmica de EDP parabólicas locais ou não locais: existência, unicidade e comportamento assintótico de solução
(Universidade Federal de São CarlosUFSCarPrograma de Pós-Graduação em Matemática - PPGMCâmpus São Carlos, 2019-07-12)
This work is dedicated to the study of dynamical properties of some partial differential equations (PDE, for short) of parabolic type, local or nonlocal ones. We prove existence, uniqueness and establish the asymptotic ...
ANALYSIS OF THE ATTAINMENT OF BOUNDARY CONDITIONS FOR A NONLOCAL DIFFUSIVE HAMILTON-JACOBI EQUATION
(2018)
We study whether the solutions of a parabolic equation with diffusion given by the fractional Laplacian and a dominating gradient term satisfy Dirichlet boundary data in the classical sense or in the generalized sense of ...