相关论文: Blow-up analysis for the generalized hyperelastic …
We establish local-in-time existence for the Euler equations on a bounded domain with space-time dependent variable coefficients, given initial data $v_0 \in H^r$ under the optimal regularity condition $r > 2.5$. In the case $r = 3$, we…
We establish the local existence and the uniqueness of solutions of the heat equation with a nonlinear boundary condition for the initial data in uniformly local $L^r$ spaces. Furthermore, we study the sharp lower estimates of the blow-up…
This paper is concerned with the energy decay and the finite time blow-up of the solution to a viscoelastic wave equation with polynomial nonlinearity and weak damping. We establish explicit and general decay results for the solutions by…
We consider a hyperbolic ordinary differential equation perturbed by a nonlinearity which can be singular at a point and in particular this includes MEMS type equations. We first study qualitative properties of the solution to the…
We investigate in this article the long-time behaviour of the solutions to the energy-dependant, spatially-homogeneous, inelastic Boltzmann equation for hard spheres. This model describes a diluted gas composed of hard spheres under…
This paper deals with the blow-up properties of positive solutions to a system of two heat equations.
We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds…
In this paper we study blow-up phenomena in general coupled nonlinear Schrodinger equations with different dispersion coefficients. We find sufficient conditions for blow-up and for the existence of global solutions. We discuss several…
In this paper, we study the Cauchy problem for a generalized integrable Camassa-Holm equation with both quadratic and cubic nonlinearity. By overcoming the difficulties caused by the complicated mixed nonlinear structure, we firstly…
In this paper, we prove the global Hadamard well-posedness of strong solutions to a non-isospectral two-component cubic Camassa-Holm system in the critical Besov space $B_{2,1}^{\frac{1}{2}}(\mathbb{T})$. Our results shows that in…
The Thermal Quasi-Geostrophic (TQG) equation is a coupled system of equations that governs the evolution of the buoyancy and the potential vorticity of a fluid. It has a local in time solution as proved in [4]. In this paper, we give a…
A non-local evolution equation of the Camassa-Holm type with dissipation is considered. The local well-posedness of the solutions of the Cauchy problem involving the equation is established via Kato's approach and the wave breaking scenario…
We study the asymptotic behaviour of solutions to the linear wave equation on cosmological spacetimes with Big Bang singularities and show that appropriately rescaled waves converge against a blow-up profile. Our class of spacetimes…
A simplified kinetic description of rapid granular media leads to a nonlocal Vlasov-type equation with a convolution integral operator that is of the same form as the continuity equations for aggregation-diffusion macroscopic dynamics.…
For one spatial variable, a new kind of nonlinear wave equation for Emden-Fowler type is considered with boundary value null and initial values. Under certain conditions on the initial data and the exponent p, we exhibit that the…
In this article, we study the perturbational method to construct the non-radially symmetric solutions of the compressible 2-component Camassa-Holm equations. In detail, we first combine the substitutional method and the separation method to…
In this paper, we consider the wave equation with variable coefficients and boundary damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy…
We partially answer a question raised by Kiselev and Zlatos in \cite{MR2180809}; in the generalized dyadic model of the Euler equation, a blow-up of $H^{1/3+\delta}$-norm occurs. We recover a few previous blow-up results for various related…
We consider the Cauchy problems in the whole space for the wave equation with a weighted L^{1}-initial data. We first derive sharp infinite time blowup estimates of the L^{2}-norm of solutions in the one and two dimensional cases. Then, we…
The \textit{parabolic scalar curvature equation} is a reaction-diffusion type equation on an $(n-1)$-manifold $\Sigma$, the time variable of which shall be denoted by $r$. Given a function $R$ on $[r_0,r_1)\times\Sigma$ and a family of…