Liu Lingyang and Gao Hang: The wellposedness and energy estimate for wave equations in domains with a space-like boundary. (2019)
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Abstract
This paper is concerned with wave equations defined in domains of R2 with an invariable left boundary and a space-like right boundary which means the right endpoint is moving faster than the characteristic. Different from the case where the endpoint moves slower than the characteristic, this problem with ordinary boundary formulations may cause ill-posedness. In this paper, we propose a new kind of boundary condition to make systems well-posed, based on an idea of transposition. The key is to prove wellposedness and a hidden regularity for the corresponding backward system. Moreover, we establish an exponential decay estimate for the energy of homogeneous systems.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2019 |
| Number: | 92 |
| ISSN: | 1417-3875 |
| Page Range: | pp. 1-19 |
| DOI: | 10.14232/ejqtde.2019.1.92 |
| Uncontrolled Keywords: | Hullámegyenlet |
| Additional Information: | Bibliogr.: p. 18-19. ; összefoglalás angol nyelven |
| Date Deposited: | 2020. Jan. 27. 13:50 |
| Last Modified: | 2021. Sep. 16. 10:42 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/66359 |
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