Displaying similar documents to “Elastic wave equation”

Long time asymptotics of the Camassa–Holm equation on the half-line

Anne Boutet de Monvel, Dmitry Shepelsky (2009)

Annales de l’institut Fourier

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We study the long-time behavior of solutions of the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation u t - u t x x + 2 u x + 3 u u x = 2 u x u x x + u u x x x on the half-line x 0 . The paper continues our study of IBV problems for the CH equation, the key tool of which is the formulation and analysis of associated Riemann–Hilbert factorization problems. We specify the regions in the quarter space-time plane x > 0 , t > 0 having qualitatively different asymptotic pictures, and give the main terms of the asymptotics in terms of...

Dispersive and Strichartz estimates for the wave equation in domains with boundary

Oana Ivanovici (2010)

Journées Équations aux dérivées partielles

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In this note we consider a strictly convex domain Ω d of dimension d 2 with smooth boundary Ω and we describe the dispersive and Strichartz estimates for the wave equation with the Dirichlet boundary condition. We obtain counterexamples to the optimal Strichartz estimates of the flat case; we also discuss the some results concerning the dispersive estimates.

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

Vladimir Georgiev (2001)

Journées équations aux dérivées partielles

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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.