The wellposedness and energy estimate for wave equations in domains with a space-like boundary

Liu, Lingyang and Gao, Hang: The wellposedness and energy estimate for wave equations in domains with a space-like boundary. Electronic journal of qualitative theory of differential equations 92. pp. 1-19. (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: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 92
Page Range: pp. 1-19
ISSN: 1417-3875
DOI: https://doi.org/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: 2020. Jan. 27. 13:50
URI: http://acta.bibl.u-szeged.hu/id/eprint/66359

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