Displaying similar documents to “Blow-up of solutions for a system of nonlinear wave equations with nonlinear damping.”

Resolvent estimates and the decay of the solution to the wave equation with potential

Vladimir Georgiev (2001)

Journées équations aux dérivées partielles

Similarity:

We prove a weighted L estimate for the solution to the linear wave equation with a smooth positive time independent potential. The proof is based on application of generalized Fourier transform for the perturbed Laplace operator and a finite dependence domain argument. We apply this estimate to prove the existence of global small data solution to supercritical semilinear wave equations with potential.