Long-term dynamics of semilinear wave equation with nonlinear localized interior damping and a source term of critical exponent

By Igor D. Chueshov, Irena Lasiecka, Daniel Toundykov. 2007

54 citations recorded by the source corpus.

This article addresses long-term behavior of solutions to a semilinear damped wave equation with a critical source term. A distinctive feature of the model is the geometrically constrained dissipation: it only affects a small subset of the domain adjacent to a connected portion of the boundary. The main result of the paper provides an affirmative answer to the open question whether global attractors for a wave equation with critical source and geometrically constrained damping are smooth and finite-dimensional. A positive answer to the same question in the case of subcritical sources was given in [9]. However, critical exponent of the source term combined with weak geometrically restricted dissipation constitutes the major new difficulty of the problem. To overcome this issue we develop a new version of Carleman's estimates and apply them in the context of recent results [12] on fractal dimension of global attractors.

Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2d1e268b8e73fe1db47f6feb41fae2ac66449f1d

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In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Attractors for wave equations with degenerate memory (2016, background): “In the same context further regularity of attractors was proved by Chueshov, Lasiecka and Toundykov [15].”