Value Problem Of Semilinear Wave Equation Research Articles

Finite time blow-up for semilinear wave equations with variable coefficients

Abstract This paper is devoted to studying initial value problems for semilinear wave equations with variable coefficients with subcritical exponents for n (n ≥ 1) space dimensions. We prove that solutions to a certain kind of subcritical wave equations cannot be global if the initial values are positive somewhere and nonnegative no matter how small the initial data are, and also we give the sharp lifespan estimate of solutions for the problems. This solves a part of the famous Strauss' conjecture about semilinear wave equations in the case of subcritical exponents and variable coefficients Cauchy problems.