Local and global wellposedness of weak solutions for the wave equation with nonlinear boundary and interior sources of supercritical exponents and damping
β Scribed by Lorena Bociu
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 511 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0362-546X
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## Abstract In this paper we investigate the global existence and finite time blowβup of solutions to the nonlinear viscoelastic equation associated with initial and Dirichlet boundary conditions. Here β__j__ denote the subβdifferential of __j__. Under suitable assumptions on __g__(Β·), __j__(Β·) an
We study the nonlinear wave equation involving the nonlinear damping term \(u_{i}\left|u_{t}\right|^{m-1}\) and a source term of type \(u|u|^{p-1}\). For \(1<p \leqslant m\) we prove a global existence theorem with large initial data. For \(1<m<p\) a blow-up result is established for sufficiently la