Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds

Abstract

In this work, we investigate the problem of finite time blow up as well as the upper bound estimates of lifespan for solutions to small-amplitude semilinear wave equations with time dependent damping and potential, and mixed nonlinearities $c_1|u_t{|}^p+c_2|u{|}^q$, posed on asymptotically Euclidean manifolds, which is related to both the Strauss conjecture and the Glassey conjecture.

arXiv comment10pages. arXiv admin note: substantial text overlap with arXiv:1912.02561

References in corpus (6)

• Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent
• Inequalities for modified Bessel functions and their integrals
• Fujita versus Strauss - a never ending story
• Lifespan of semilinear wave equation with scale invariant dissipation and mass and sub-Strauss power nonlinearity
• Nonexistence of global solutions of wave equations with weak time-dependent damping and combined nonlinearity
• Heat-like and wave-like lifespan estimates for solutions of semilinear damped wave equations via a Kato's type lemma