Analysis of damped wave equations with critical non linearity with life span de- termination

Abstract

In this thesis the analysis and life span determination of damped wave equation with critical non linearity was successfully implemented in lower dimension n 3. Analytical technique for blow-up phenomena and prove of upper estimate and lower estimate of solution to damped wave equation with critical non linearity is presented. The critical non linearity is extended to study this problem. The method of proving the estimates is test function method than iteration argument. Some theorems and propositions are given to demonstrate the applicability and importance of this method. The obtained analytical results reveal that the solution is well-posed in a nite time and the test function method is very good than other methods in proving the life span estimate of damped wave equation with critical non linearity and it reduce complexity arising from the critical power