Global existence for semilinear damped wave equations in relation with the Strauss conjecture

Abstract

We study the global existence of solutions to semilinear wave equations with power-type nonlinearity and general lower order terms on $n$ dimensional nontrapping asymptotically Euclidean manifolds, when $n=3,4$. In addition, we prove almost global existence with sharp lower bound of the lifespan for the four dimensional critical problem.

12 pages, no figure

References in corpus (3)

• Concerning the Strauss conjecture on asymptotically Euclidean manifolds
• Blow-up of solutions to critical semilinear wave equations with variable coefficients
• On the blow-up for critical semilinear wave equations with damping in the scattering case

Cited by in corpus (3)

• Lifespan of semilinear generalized Tricomi equation with Strauss type exponent
• On the blow-up for critical semilinear wave equations with damping in the scattering case
• Short time blow-up by negative mass term for semilinear wave equations with small data and scattering damping