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Wenhui Chen

Publications and source records attributed to Wenhui Chen.

78 records · Page 5Linked to original sources
arXiv2019

Dissipative structure and diffusion phenomena for doubly dissipative elastic waves in two space dimensions

In this paper we study the Cauchy problem for doubly dissipative elastic waves in two space dimensions, where the damping terms consist of two different friction or structural damping. We derive energy estimates and diffusion phenomena with different assumptions on initial data. Particularly, we find the dominant influence on diffusion phenomena by introducing a new threshold of diffusion structure.

math.AP↗
arXiv2019

Cauchy problem for thermoelastic plate equations with different damping mechanisms

In this paper we study Cauchy problem for thermoelastic plate equations with friction or structural damping in $\mathbb{R}^n$, $n\geq1$, where the heat conduction is modeled by Fourier's law. We explain some qualitative properties of solutions influenced by different damping mechanisms. We show which damping in the model has a dominant influence on smoothing effect, energy estimates, $L^p-L^q$ estimates not necessary on the conjugate line, and on diffusion phenomena. Moreover, we derive asymptotic profiles of solutions in a framework of weighted $L^1$ data. In particular, sharp decay estimates for lower bound and upper bound of solutions in the $\dot{H}^s$ norm ($s\geq0$) are shown.

math.AP↗
arXiv2018

An application of $L^m-L^r$ estimates to weakly coupled systems of semilinear viscoelastic wave equations

We consider weakly coupled systems of semilinear viscoelastic wave equations with different power source nonlinearities in $\mathbb{R}^n$, $n\geq1$ as follows: \begin{equation*} \left\{\begin{aligned} &u_{tt}-Δu+g\astΔu+u_t=|\partial_t^{\ell}v|^p,\\ &v_{tt}-Δv+g\astΔv+v_t=|\partial_t^{\ell}u|^q,\\ \end{aligned}\right. \end{equation*} with $\ell=0,1$ and $p,q>1$. After presenting $L^m-L^r$ estimates with $1\leq m\leq r\leq \infty$ of solutions to the corresponding linearized problem with vanishing right-hand side, we prove the existence of global in time solutions to the weakly coupled systems, where the initial data are supposed to belong to different $L^r$ spaces with different additional $L^m$ regularities.

math.AP↗
arXiv2018

Weakly coupled systems of semi-linear elastic waves with different damping mechanisms in 3D

We consider the following Cauchy problem for weakly coupled systems of semi-linear damped elastic waves with a power source non-linearity in three-dimensions: \begin{equation*} U_{tt}-a^2ΔU-\big(b^2-a^2\big)\nabla\text{div } U+(-Δ)^θU_t=F(U),\,\, (t,x)\in[0,\infty)\times\mathbb{R}^3, \end{equation*} where $U=U(t,x)=\big(U^{(1)}(t,x),U^{(2)}(t,x),U^{(3)}(t,x)\big)^{\mathrm{T}}$ with $b^2>a^2>0$ and $θ\in[0,1]$. Our interests are some qualitative properties of solutions to the corresponding linear model with vanishing right-hand side and the influence of the value of $θ$ on the exponents $p_1,p_2,p_3$ in $F(U)=\big(|U^{(3)}|^{p_1},|U^{(1)}|^{p_2},|U^{(2)}|^{p_3}\big)^{\mathrm{T}}$ to get results for the global (in time) existence of small data solutions.

math.AP↗
arXiv2018

Weakly coupled system of semilinear wave equations with distinct scale-invariant terms in the linear part

In this work we determine the critical exponent for a weakly coupled system of semilinear wave equations with distinct scale-invariant lower order terms, when these terms make both equations in some sense parabolic-like. For the blow-up result the test functions method is applied, while for the global existence (in time) results we use L2-L2 estimates with additional L1 regularity.

math.AP↗