Decay Estimates for Fourth Order Wave Equations
โ Scribed by Steven Paul Levandosky
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 701 KB
- Volume
- 143
- Category
- Article
- ISSN
- 0022-0396
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
## 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
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