HOẠT ĐỘNG TRONG TUẦN

Thời gian: 9h30, Thứ 3 ngày 12/4/2021

Link: https://meet.google.com/puo-ghwc-uux?pli=1&authuser=1

Tóm tắt: In this talk, we mainly investigate lifespan estimates for solutions to the Cauchy problem for the weakly coupled system of semilinear damped wave equations in the critical case, the open question and not so far known. By using a suitable test function method associated with nonlinear differential inequalities, we catch upper bound estimates for the lifespan. Moreover, we establish polynomial-logarithmic type time-weighted Sobolev spaces to obtain lower bound estimates for the lifespan in low spatial dimensions. Then, together with the derived lifespan estimates, completely new and sharp results on estimates for the lifespan in the critical case are claimed. Finally, we give an application of our results to the semilinear reaction-diffusion system in the critical case.