Journal
CHINESE ANNALS OF MATHEMATICS SERIES B
Volume 23, Issue 2, Pages 253-266Publisher
SHANGHAI SCIENTIFIC TECHNOLOGY LITERATURE PUBLISHING HOUSE
DOI: 10.1142/S0252959902000249
Keywords
hyperbolic obstacle problem; linear hyperbolic operator; strong solution
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This paper presents new results for strong solutions and their coincidence sets of the obstacle problem for linear hyperbolic operators of first order. An inequality similar to the Lewy-Stampacchia ones for elliptic and parabolic problems is shown. Under nondegeneracy conditions the stability of the coincidence set is shown with respect to the variation of the data and with respect to approximation by semilinear hyperbolic problems. These results are applied to the asymptotic stability of the evolution problem with respect to the stationary coercive problem with obstacle.
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