Finite dimensionality and regularity of attractors for a 2-D semilinear wave equation with nonlinear dissipation |
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| Authors: | Irena Lasiecka Anastasia A Ruzmaikina |
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| Institution: | Department of Mathematics, University of Virginia, Kerchof Hall, Charlottesville, VA 22903, USA |
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| Abstract: | We consider a semilinear wave equation, defined on a two-dimensional bounded domain Ω, with a nonlinear dissipation. Our main result is that the flow generated by the model is attracted by a finite dimensional global attractor. In addition, this attractor has additional regularity properties that depend on regularity properties of nonlinear functions in the equation. To our knowledge this is a first result of this type in the context of higher dimensional wave equations. |
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| Keywords: | Semilinear wave equation Nonlinear dissipation Global attractors Finite dimensional attractors Regularity of attractors |
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