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November/December 2018 A classification for wave models with time-dependent potential and speed of propagation
Marcelo Rempel Ebert, Wanderley Nunes do Nascimento
Adv. Differential Equations 23(11/12): 847-888 (November/December 2018).

Abstract

In this paper, we study the long time behavior of energy solutions for a class of wave equation with time-dependent potential and speed of propagation. We introduce a classification of the potential term, which clarifies whether the solution behaves like the solution to the wave equation or Klein-Gordon equation. Moreover, the derived linear estimates are applied to obtain global (in time) small data energy solutions for the Cauchy problem to semilinear Klein-Gordon models with power nonlinearity.

Citation

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Marcelo Rempel Ebert. Wanderley Nunes do Nascimento. "A classification for wave models with time-dependent potential and speed of propagation." Adv. Differential Equations 23 (11/12) 847 - 888, November/December 2018.

Information

Published: November/December 2018
First available in Project Euclid: 25 September 2018

zbMATH: 06982201
MathSciNet: MR3857872

Subjects:
Primary: 35B40 , 35L15 , 35L71

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.23 • No. 11/12 • November/December 2018
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