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- W2887029579 abstract "The present paper is a continuation of our recent paper cite{DaoReissig}. We will consider the following Cauchy problems for semi-linear structurally damped $sigma$-evolution models: begin{equation*} u_{tt}+ (-Delta)^sigma u+ mu (-Delta)^delta u_t = f(u,u_t),, u(0,x)= u_0(x),, u_t(0,x)=u_1(x) end{equation*} with $sigma ge 1$, $mu>0$ and $delta in (frac{sigma}{2},sigma]$. Our aim is to study two main models including $sigma$-evolution models with structural damping $delta in (frac{sigma}{2},sigma)$ and those with visco-elastic damping $delta=sigma$. Here the function $f(u,u_t)$ stands for power nonlinearities $|u|^{p}$ and $|u_t|^{p}$ with a given number $p>1$. We are interested in investigating the global (in time) existence of small data solutions to the above semi-linear models from suitable spaces basing on $L^q$ space by assuming additional $L^{m}$ regularity on the initial data, with $qin (1,infty)$ and $min [1,q)$." @default.
- W2887029579 created "2018-08-22" @default.
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- W2887029579 date "2018-08-15" @default.
- W2887029579 modified "2023-09-27" @default.
- W2887029579 title "$L^1$ estimates for oscillating integrals and their applications to semi-linear models with $sigma$-evolution like structural damping" @default.
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