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Existence and asymptotic behavior for a singular parabolic equation
(Amer Mathematical SocProvidenceEUA, 2005)
Semilinear parabolic problems in thin domains with a highly oscillatory boundary
(Pergamon-Elsevier B.V. Ltd, 2011-10-01)
In this paper, we study the behavior of the solutions of nonlinear parabolic problems posed in a domain that degenerates into a line segment (thin domain) which has an oscillating boundary. We combine methods from linear ...
Continuity of attractors for parabolic problems with localized large diffusion
(PERGAMON-ELSEVIER SCIENCE LTD, 2008)
In this paper we study the continuity of asymptotics of semilinear parabolic problems of the form u(t) - div(p(x)del u) + lambda u =f(u) in a bounded smooth domain ohm subset of R `` with Dirichlet boundary conditions when ...
Space-Time Least-Squares Finite Element Methods for Parabolic Distributed Optimal Control Problems
(WALTER DE GRUYTER GMBH, 2024)
We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order optimality condition by a recently developed ...
Patterns in parabolic problems with nonlinear boundary conditions
(Elsevier B.V., 2007-01-15)
We obtain existence of asymptotically stable nonconstant equilibrium solutions for semilinear parabolic equations with nonlinear boundary conditions on small domains connected by thin channels. We prove the convergence of ...