Decay property of solutions for damped wave equations with space–time dependent damping term

Abstract: We consider the Cauchy problem for the damped wave equation with space–time dependent potential and absorbing semilinear term . Here, with , and . Using the weighted energy method, we can obtain the decay rate of the solution, which is almost optimal in the case . Combining this decay rate with the result that we got in the paper [J. Lin, K. Nishihara, J. Zhai, -estimates of solutions for damped wave equations with space–time dependent damping term, J. Differential Equations 248 (2010) 403–422], we believe that is a critical exponent. Note that when , coincides to the Fujita exponent . The new points include the estimate in the supercritical exponent and for not necessarily compactly supported data. [ABSTRACT FROM AUTHOR]