We study decay estimates for the solutions and their derivatives to the initial value problems for some generalized nonlinear evolution equations which have lower order diffusion terms. 1995 Academic Press. Inc.
Some decay-estimates for nonlinear wave equations
โ Scribed by Wolf von Wahl
- Publisher
- Elsevier Science
- Year
- 1972
- Tongue
- English
- Weight
- 201 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract Let __u__ and __v__ be, respectively, the solutions to the Cauchy problems for the dissipative wave equation $$u\_{tt}+u\_tโ\Delta u=0$$\nopagenumbers\end and the heat equation $$v\_tโ\Delta v=0$$\nopagenumbers\end We show that, as $t\rightarrow+\infty$\nopagenumbers\end, the norms
We present new decay estimates of solutions for the mixed problem of the equation vtt -vxx + vt = 0, which has the weighted initial data [v . Similar decay estimates are also derived to the Cauchy problem in R N for utt -u+ut = 0 with the weighted initial data. Finally, these decay estimates can be
## Abstract We study the electromagnetic wave equation and the perturbed massless Dirac equation on โ~__t__~ ร โ^3^: where the potentials __A__(__x__), __B__(__x__), and __V__(__x__) are assumed to be small but may be rough. For both equations, we prove the expected time decay rate of the solution