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
