Continuity of the set equilibria of non-autonomous damped wave equations with terms concentrating on the boundary

Flank D. M. Bezerra; Gleiciane da Silva Aragão

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arXiv · 1808.05667

Continuity of the set equilibria of non-autonomous damped wave equations with terms concentrating on the boundary

Flank D. M. Bezerra·Gleiciane da Silva Aragão

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Abstract

In this paper we are interested in the behavior of the solutions of non-autonomous damped wave equations when some reaction terms are concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary as a parameter \varepsilon goes to zero. We prove the conti- nuity of the set equilibria of these equations. Moreover, if an equilibrium solution of the limit problem is hyperbolic, then we show that the per- turbed equation has one and only one equilibrium solution nearby.

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Flank D. M. Bezerra, Gleiciane da Silva Aragão. 2018-08-16. Continuity of the set equilibria of non-autonomous damped wave equations with terms concentrating on the boundary. https://arxiv.org/abs/1808.05667

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