Displaying similar documents to “Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation. II”

Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation

Paolo Secchi (2004)

Bollettino dell'Unione Matematica Italiana

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We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition. We are interested to the asymptotic behavior for large times for the solution, and in particular to the dependence on the norms of the initial data in the estimate for the pointwise decay rate. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.

Null Condition for Semilinear Wave Equation with Variable Coefficients

Catalano, Fabio (1999)

Serdica Mathematical Journal

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∗The author was partially supported by M.U.R.S.T. Progr. Nazionale “Problemi Non Lineari...” In this work we analyse the nonlinear Cauchy problem (∂tt − ∆)u(t, x) = ( λg + O(1/(1 + t + |x|)^a) ) ) ∇t,x u(t, x), ∇t,x u(t, x) ), whit initial data u(0, x) = e u0 (x), ut (0, x) = e u1 (x). We assume a ≥ 1, x ∈ R^n (n ≥ 3) and g the matrix related to the Minkowski space. It can be considerated a pertubation of the case when the quadratic term has constant coefficient...