The existence and uniqueness are proved for global classical solutions of the spatially periodic Cauchy problem to the following system of parabolic equations s y y ␣ y q ␣ Ž . which was proposed as a substitute for the Rayleigh᎐Benard equation and can lead to Lorenz equations.
Some remarks on global existence to the Cauchy problem of the wave equation with nonlinear dissipation
✍ Scribed by Nour-Eddine Amroun; Abbès Benaissa
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 160 KB
- Volume
- 281
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
In this paper we prove the existence of global decaying H^2^ solutions to the Cauchy problem for a wave equation with a nonlinear dissipative term by constructing a stable set in H^1^(ℝ^n^ ). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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