Differential and Integral Equations

Global existence for semilinear damped wave equations in the scattering case

Yige Bai and Mengyun Liu

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Abstract

We study the global existence of solutions to semilinear damped wave equations in the scattering case with power-type nonlinearity on the derivatives, posed on nontrapping asymptotically Euclidean manifolds. The main idea is to shift initial time by local existence. As a result, we could convert the damping term to small enough perturbation and obtain the global existence.

Article information

Source
Differential Integral Equations, Volume 32, Number 3/4 (2019), 233-248.

Dates
First available in Project Euclid: 23 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.die/1548212431

Mathematical Reviews number (MathSciNet)
MR3909986

Zentralblatt MATH identifier
07036982

Subjects
Primary: 35L05: Wave equation 35L15: Initial value problems for second-order hyperbolic equations 35L71: Semilinear second-order hyperbolic equations

Citation

Bai, Yige; Liu, Mengyun. Global existence for semilinear damped wave equations in the scattering case. Differential Integral Equations 32 (2019), no. 3/4, 233--248. https://projecteuclid.org/euclid.die/1548212431


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