Tuan Anh Dao
Published 2019-08-22Version 1
In this paper, we are interested in analyzing the asymptotic profiles of solutions to the Cauchy problem for linear structurally damped $\sigma$-evolution equations in $L^2$-sense. Depending on the parameters $\sigma$ and $\delta$ we would like to not only indicate approximation formula of solutions but also recognize the optimality of their decay rates as well in the distinct cases of parabolic like damping and $\sigma$-evolution like damping. Moreover, such results are also discussed when we mix these two kinds of damping terms in a $\sigma$-evolution equation to investigate how each of them affects the asymptotic profile of solutions.
Asymptotic profiles for the Cauchy problem of damped beam equation with two variable coefficients and derivative nonlinearity
Reaction diffusion equations with super-linear absorption: universal bounds, uniqueness for the Cauchy problem, boundedness of stationary solutions
Well-posedness of the Cauchy problem for the fractional power dissipative equations
![QR code for arXiv:1908.08492 [math.AP]](http://oss.arxitics.com/images/favicon.svg)