On the long time behaviour of solutions to dissipative wave equations in \(\mathbb{R}^{2}\) (Q2433291)
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scientific article
| Language | Label | Description | Also known as |
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| English | On the long time behaviour of solutions to dissipative wave equations in \(\mathbb{R}^{2}\) |
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On the long time behaviour of solutions to dissipative wave equations in \(\mathbb{R}^{2}\) (English)
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27 October 2006
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To study the long time behaviour of solutions to the Cauchy problem for the dissipative wave equation, the author uses a method he applied for studying the same problem for the convection-diffusion equation, in a previous paper [Rend. Mat. Appl., VII. Ser. 23, No. 1, 163--188 (2003; Zbl 1047.35057)]. The method consists of two steps: a parabolic time-dependent scaling and the construction of a non-negative functional which gives information on the evolution of solution for the transformed problem.
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Wave equation
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Cauchy problem
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long time behaviour
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linear damping
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parabolic time-dependent scaling
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