Sharp lifespan estimates for the weakly coupled system of semilinear damped wave equations in the critical case

The open question, which seems to be also the final part, in terms of studying Cauchy problem for weakly coupled system damped wave equations or reaction-diffusion equations, is so far known as sharp lifespan estimates critical case. In this paper, we mainly investigate solutions semilinear By using a suitable test function method associated with nonlinear differential inequalities, catch upper bound lifespan. Moreover, establish polynomial-logarithmic type time-weighted Sobolev spaces obtain lower low spatial dimensions. Then, together derived estimates, new and results on case are claimed. Finally, give an application our