GLOBAL EXISTENCE AND Lp ESTIMATES FOR SOLUTIONS OF DAMPED WAVE EQUATION WITH NONLINEAR CONVECTION IN#br#
MULTI-DIMENSIONAL SPACE

doi:10.1016/S0252-9602(12)60089-7

Abstract

Abstract:

In this article, the author studies the Cauchy problem of the damped wave equation with a nonlinear convection term in multi-dimensions. The author shows that a classical solution to the Cauchy problem exists globally in time under smallness condition on the initial perturbation. Furthermore, the author obtains the L^p (2≤ p ≤ ∞) decay estimates of the solution.

Key words: Damped wave equation with nonlinear convection, frequency decomposition method, Greens function, energy method, global existence

CLC Number:

35L70

CHEN Jiao. GLOBAL EXISTENCE AND L^p ESTIMATES FOR SOLUTIONS OF DAMPED WAVE EQUATION WITH NONLINEAR CONVECTION IN#br# MULTI-DIMENSIONAL SPACE[J].Acta mathematica scientia,Series B, 2012, 32(3): 1167-1180.

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