0010-13640/81/00344029S2.30 'I$ need not even be defined for all arguments, since u' and u" will stay small for sufficiently small norms off, g. 2Solutions of the one-dimensional problem (4a, b) can also be viewed as special solutions u(x.r) of the n-dimensional equation u,, = c(u,,)Au which happen
Blow-up for semilinear wave equations in four or five space dimensions
โ Scribed by Hiroyuki Takamura
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 409 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## For suitable and F, we prove that all classical solutions of the quasilinear wave equation RR !( ( V )) V "F(), with initial data of compact support, develop singularities in "nite time. The assumptions on and F include in particular the model case O>, for q\*2, and "$1. The starting point of
We consider the semilinear wave equation in the radial case with conformal subcritical power nonlinearity. If we consider a blow-up point different from the origin, then we exhibit a new Lyapunov functional which is a perturbation of the one-dimensional case and extend all our previous results known
Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku, Tokyo 169, Japan