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Almost global existence to nonlinear wave equations in three space dimensions

✍ Scribed by F. John; S. Klainerman

Publisher
John Wiley and Sons
Year
1984
Tongue
English
Weight
434 KB
Volume
37
Category
Article
ISSN
0010-3640

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πŸ“œ SIMILAR VOLUMES

On almost global existence for nonrelati
On almost global existence for nonrelativistic wave equations in 3D
✍ Sergiu Klainerman; Thomas C. Sideris πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 507 KB

Almost global solutions are constructed to three-dimensional, quadratically nonlinear wave equations. The proof relies on generalized energy estimates and a new decay estimate. The method applies to equations that are only classically invariant, such as the nonlinear system of hyperelasticity. @ 199

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## Abstract In this paper the nonlinear viscoelastic wave equation associated with initial and Dirichlet boundary conditions is considered. Under suitable conditions on __g__, it is proved that any weak solution with negative initial energy blows up in finite time if __p__ > __m__. Also the case o