Advances in Differential Equations

A classification for wave models with time-dependent potential and speed of propagation

Marcelo Rempel Ebert and Wanderley Nunes do Nascimento

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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.

Article information

Adv. Differential Equations, Volume 23, Number 11/12 (2018), 847-888.

First available in Project Euclid: 25 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L15: Initial value problems for second-order hyperbolic equations 35B40: Asymptotic behavior of solutions 35L71: Semilinear second-order hyperbolic equations


Ebert, Marcelo Rempel; Nascimento, Wanderley Nunes do. A classification for wave models with time-dependent potential and speed of propagation. Adv. Differential Equations 23 (2018), no. 11/12, 847--888.

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