Uniform Energy Decay for Wave Equations with Unbounded Damping Coefficients

Abstract

We consider the Cauchy problem for wave equations with unbounded damping coefficients in Rⁿ. For a general class of unbounded damping coefficients, we derive uniform total energy decay estimates together with a unique existence result of a weak solution. In this case we never impose strong assumptions such as compactness of the support of the initial data. This means that we never rely on the finite propagation speed property of the solutions, and we try to deal with an essential unbounded coefficient case. One of our methods comes from an idea developed in [9].