Displaying similar documents to “An existence theorem for an implicit nonlinear evolution equation.”

Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria

Felipe Alvarez, Hedy Attouch (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction...

Reliable solution of parabolic obstacle problems with respect to uncertain data

Ján Lovíšek (2003)

Applications of Mathematics

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A class of parabolic initial-boundary value problems is considered, where admissible coefficients are given in certain intervals. We are looking for maximal values of the solution with respect to the set of admissible coefficients. We give the abstract general scheme, proposing how to solve such problems with uncertain data. We formulate a general maximization problem and prove its solvability, provided all fundamental assumptions are fulfilled. We apply the theory to certain Fourier...

Periodic solutions of a nonlinear evolution problem

Nelson Nery Oliveira Castro, Nirzi G. de Andrade (2002)

Applications of Mathematics

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In this paper we prove existence of periodic solutions to a nonlinear evolution system of second order partial differential equations involving the pseudo-Laplacian operator. To show the existence of periodic solutions we use Faedo-Galerkin method with a Schauder fixed point argument.