Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation
2003 ◽
Vol 2003
(8)
◽
pp. 409-427
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Keyword(s):
We study the effects of large diffusivity in all parts of the domain in a linearly damped wave equation subject to standard zero Robin-type boundary conditions. In the linear case, we show in a given sense that the asymptotic behaviour of solutions verifies a second-order ordinary differential equation. In the semilinear case, under suitable dissipative assumptions on the nonlinear term, we prove the existence of a global attractor for fixed diffusion and that the limiting attractor for large diffusion is finite dimensional.
1964 ◽
Vol 281
(1385)
◽
pp. 184-206
◽
1982 ◽
Vol 37
(8)
◽
pp. 830-839
◽