A note on the lifespan of solutions to the semilinear damped wave equation

Abstract

This paper concerns estimates of the lifespan of solutions to the semilinear damped wave equation. We give upper estimates of the lifespan for the semilinear damped wave equation with variable coefficients in all space dimensions.

9 pages

References in corpus (3)

• Small data global existence for the semilinear wave equation with space-time dependent damping
• A modified test function method for damped waves
• Lifespan of solutions for the nonlinear Schrödinger equation without gauge invariance

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