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
Global Nonexistence for the Cauchy Problem of Some Nonlinear Reaction–Diffusion Systems
✍ Scribed by Mokhtar Kirane; Mahmoud Qafsaoui
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 187 KB
- Volume
- 268
- Category
- Article
- ISSN
- 0022-247X
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## 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)
It is well known that, for reaction-diffusion systems, if the nonlinearities grow faster than a polynomial, nothing seems to be known for instance. The purpose of this paper is to give sufficient conditions guaranteeing global existence, uniqueness and uniform boundedness of solutions for coupled re