Displaying similar documents to “ N -wave equations with orthogonal algebras: 2 and 2 × 2 reductions and soliton solutions.”

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.