Displaying similar documents to “Weak periodic solutions of some quasilinear parabolic equations with data measures.”

Weak solutions of a parabolic-elliptic type system for image inpainting

Zhengmeng Jin, Xiaoping Yang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider the initial boundary value problem of a parabolic-elliptic system for image inpainting, and establish the existence and uniqueness of weak solutions to the system in dimension two.

Classical global solutions of the initial boundary value problems for a class of nonlinear parabolic equations

Guo Wang Chen (1994)

Commentationes Mathematicae Universitatis Carolinae

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The existence, uniqueness and regularities of the generalized global solutions and classical global solutions to the equation u t = - A ( t ) u x 4 + B ( t ) u x 2 + g ( u ) x 2 + f ( u ) x + h ( u x ) x + G ( u ) with the initial boundary value conditions u ( - ℓ , t ) = u ( ℓ , t ) = 0 , u x 2 ( - ℓ , t ) = u x 2 ( ℓ , t ) = 0 , u ( x , 0 ) = ϕ ( x ) , or with the initial boundary value conditions u x ( - ℓ , t ) = u x ( ℓ , t ) = 0 , u x 3 ( - ℓ , t ) = u x 3 ( ℓ , t ) = 0 , u ( x , 0 ) = ϕ ( x ) , are proved. Moreover, the asymptotic behavior of these solutions is considered under some conditions.

Positive periodic solutions of parabolic evolution problems: a translation along trajectories approach

Aleksander Ćwiszewski (2011)

Open Mathematics

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A translation along trajectories approach together with averaging procedure and topological degree are used to derive effective criteria for existence of periodic solutions for nonautonomous evolution equations with periodic perturbations. It is shown that a topologically nontrivial zero of the averaged right hand side is a source of periodic solutions for the equations with increased frequencies. Our setting involves equations on closed convex cones, therefore it enables us to study...

Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations

Eduard Feireisl (1990)

Aplikace matematiky

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In the present paper, the existence of a weak time-periodic solution to the nonlinear telegraph equation U t t + d U t - σ ( x , t , U x ) x + a U = f ( x , t , U x , U t , U ) with the Dirichlet boundary conditions is proved. No “smallness” assumptions are made concerning the function f . The main idea of the proof relies on the compensated compactness theory.