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pro vyhledávání: '"Reissig, Michael"'
In this paper, we would like to consider the Cauchy problem for a weakly coupled system of semi linear $sigma$ evolution equations with different damping mechanisms for any $\sigma>1$, parabolic like damping and $\sigma$ evolution like damping. Motiv
Externí odkaz:
http://arxiv.org/abs/2406.00450
Autor:
Aslan, Halit Sevki, Reissig, Michael
In this paper, we study the following Cauchy problem for linear visco-elastic damped wave models with a general time-dependent coefficient $g=g(t)$: \begin{equation} \label{EqAbstract} \tag{$\star$} \begin{cases} u_{tt}- \Delta u + g(t)(-\Delta)u_t=0
Externí odkaz:
http://arxiv.org/abs/2307.12340
Autor:
Chen, Wenhui, Reissig, Michael
In this paper, we consider the Cauchy problem for semilinear classical wave equations \begin{equation*} u_{tt}-\Delta u=|u|^{p_S(n)}\mu(|u|) \end{equation*} with the Strauss exponent $p_S(n)$ and a modulus of continuity $\mu=\mu(\tau)$, which provide
Externí odkaz:
http://arxiv.org/abs/2306.11471
Autor:
Chen, Wenhui, Reissig, Michael
We study semilinear damped wave equations with power nonlinearity $|u|^p$ and initial data belonging to Sobolev spaces of negative order $\dot{H}^{-\gamma}$. In the present paper, we obtain a new critical exponent $p=p_{\mathrm{crit}}(n,\gamma):=1+\f
Externí odkaz:
http://arxiv.org/abs/2108.05667
Autor:
Dao, Tuan Anh, Reissig, Michael
We would like to study a weakly coupled system of semi-linear classical damped wave equations with moduli of continuity in nonlinearities whose powers belong to the critical curve in the $p-q$ plane. The main goal of this paper is to find out the sha
Externí odkaz:
http://arxiv.org/abs/2007.04157
Autor:
Chen, Wenhui, Reissig, Michael
In this paper, we consider blow-up behavior of weak solutions to a weakly coupled system for a semilinear damped wave equation and a semilinear wave equation in $\mathbb{R}^n$. This problem is part of the so-called Nakao's problem proposed by Profess
Externí odkaz:
http://arxiv.org/abs/2001.01533
Akademický článek
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Autor:
Dao, Tuan Anh, Reissig, Michael
We would like to prove a blow-up result for semi-linear structurally damped $\sigma$-evolution equations, where $\sigma \ge 1$ and $\delta\in [0,\sigma)$ are assumed to be any fractional numbers. To deal with the fractional Laplacian operators $(-\De
Externí odkaz:
http://arxiv.org/abs/1909.01181
Autor:
Chen, Wenhui, Reissig, Michael
In this note we try to understand the blow-up of solutions to Nakao's problem by using nonlinear ordinary differential inequalities.
Comment: Up to now, this note only contains some remarks.16 pages
Comment: Up to now, this note only contains some remarks.16 pages
Externí odkaz:
http://arxiv.org/abs/1904.03938
In this paper we consider the Cauchy problem for the semilinear damped wave equation $u_{tt}-\Delta u + u_t = h(u);\qquad u(0;x) = f(x); \quad u_t(0;x) = g(x);$ where $h(s) = |s|^{1+2/n}\mu(|s|)$. Here n is the space dimension and $\mu$ is a modulus
Externí odkaz:
http://arxiv.org/abs/1904.02939