Related papers: $L^p$-$L^q$ decay estimates for dissipative linear…
In this paper we focus on the initial value problem for quasi-linear dissipative plate equation in multi-dimensional space $(n\geq2)$. This equation verifies the decay property of the regularity-loss type, which causes the difficulty in…
This paper mainly investigates the Cauchy problem of the spatially weighted dissipative equation with initial data in the weighted Lebesgue space. A generalized Hankel Transform is introduced to derive the analytical solution and a special…
We study the large time behavior of solutions near a constant equilibrium to the compressible Euler-Maxwell system in $\r3$. We first refine a global existence theorem by assuming that the $H^3$ norm of the initial data is small, but the…
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 +…
In this paper we deal with the long time existence for the Cauchy problem associated to some asymptotic models for long wave, small amplitude gravity surface waves. We generalize some of the results that can be found in the literature…
In this paper, we are concerned with the 2D damped wave-type magnetohydrodynamic system (abbreviated as MHD-wave system). The purpose of this paper is to study the large time behavior of solutions to the MHD-wave system, espesically to…
We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
We consider the system of elastic waves with critical space dependent damping $V(x)$. We study the Cauchy problem for this model in the $2$-dimensional Euclidean space ${\bf R}^{2}$, and we obtain faster decay rates of the total energy as…
In this paper we analyze the large-time behavior of the augmented Burgers equation. We first study the well-posedness of the Cauchy problem and obtain $L^1$-$L^p$ decay rates. The asymptotic behavior of the solution is obtained by showing…
This paper studies the diffusion approximation, non-equilibrium model of radiation hydrodynamics derived by Buet and Despr\'es (J. Quant. Spectrosc. Radiat. Transf. 85 (2004), no. 3-4, 385-418). The latter describes a non-relativistic…
We consider the strictly hyperbolic Cauchy problem \begin{align*} &D_t^m u - \sum\limits_{j = 0}^{m-1} \sum\limits_{|\gamma|+j = m} a_{m-j,\,\gamma}(t,\,x) D_x^\gamma D_t^j u = 0, \newline &D_t^{k-1}u(0,\,x) = g_k(x),\,k = 1,\,\ldots,\,m,…
We consider the large time asymptotic behavior of the global solutions to the initial value problem for the nonlinear damped wave equation with slowly decaying initial data. When the initial data decay fast enough, it is known that the…
We consider the Cauchy problem for the evolutive discrete p-Laplacian in infinite graphs, with initial data decaying at infinity. We prove optimal sup and gradient bounds for nonnegative solutions, when the initial data has finite mass, and…
We prove several integral Harnack-type inequalities for local weak solutions of parabolic equations with measurable and bounded coefficients, describing singular s-fractional p-Laplacian diffusion. Then we apply the aforementioned estimates…
In this paper, we investigate the initial value problem for symmetric hyperbolic systems on globally hyperbolic Lorentzian manifolds with potentials that are both nonlocal in time and space. When the potential is retarded and uniformly…
At the core of this article is an improved, sharp dispersive estimate for the anisotropic linear semigroup $e^{R_1 t}$ arising in both the study of the dispersive SQG equation and the inviscid Boussinesq system. We combine the decay…
We compute the sharp time decay rates of the solutions of the IVP for quasi-geostrophic equation and the Boussinesq model, subject to fractional dissipation. Moreover, we explicitly identify the asymptotic profiles, the kernel of the…
This paper investigates the initial-boundary value problem for weakly coupled systems of time-fractional subdiffusion equations with spatially and temporally varying coupling coefficients. By combining the energy method with the coercivity…
We consider the non-cutoff Boltzmann equation in the spatially inhomogeneous, soft potentials regime, and establish decay estimates for large velocity. In particular, we prove that pointwise algebraically decaying upper bounds in the…
We obtain new $L^1$ contraction results for bounded entropy solutions of Cauchy problems for degenerate parabolic equations. The equations we consider have possibly strongly degenerate local or non-local diffusion terms. As opposed to…