## 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^(β^__n__^ ). (Β© 2008 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
Global Smooth Solutions to the Spatially Periodic Cauchy Problem for Dissipative Nonlinear Evolution Equations
β Scribed by Ling Hsiao; Huaiyu Jian
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 214 KB
- Volume
- 213
- Category
- Article
- ISSN
- 0022-247X
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β¦ Synopsis
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 β£ y q β£ Ε½ .
which was proposed as a substitute for the RayleighαBenard equation and can lead to Lorenz equations.
π SIMILAR VOLUMES
The paper studies the existence and nonexistence of global solutions to the Cauchy problem for a nonlinear beam equation arising in the model in variational form for the neo-Hookean elastomer rod where k 1 ,k 2 > 0 are real numbers, g(s) is a given nonlinear function. When g(s) = s n (where n 2 is