相关论文: The Cauchy problem for the standard one pressure s…

For the natural initial conditions $L^1$ in the density field (more generally a positive bounded Radon measure) and $L^\infty$ in the velocity field we obtain global approximate solutions to the Cauchy problem for the 3-D systems of…

We study numerically the standard one pressure model of two fluid flows with energy equations. This system is not solved in time derivative. It has been transformed into an equivalent system solved in time derivative. We show that the…

We investigate existence and uniqueness of weak solutions of the Cauchy problem for the porous medium equation on negatively curved Riemannian manifolds. We show existence of solutions taking as initial condition a finite Radon measure, not…

We prove existence and uniqueness for a class of signed Radon measure-valued entropy solutions of the Cauchy problem for a first order scalar hyperbolic conservation law in one space dimension. The initial data of the problem is a finite…

We prove existence and uniqueness of Radon measure-valued solutions of the Cauchy problem $$ \begin{cases} u_t+[\varphi(u)]_x=0 & \text{in } \mathbb{R}\times (0,T) \\ u=u_0\ge 0 &\text{in } \mathbb{R}\times \{0\}, \end{cases} $$ where $u_0$…

We proposed rigorous definitions of Radon measure solutions for boundary value problems of steady compressible Euler equations which modeling hypersonic-limit inviscid flows passing two-dimensional ramps, and their interactions with still…

In this paper, we are interested to an inverse Cauchy problem governed by the Stokes equation, called the data completion problem. It consists in determining the unspecified fluid velocity, or one of its components over a part of its…

We prove convergence of solutions to the parabolic Allen-Cahn equation to Brakke's motion by mean curvature in space forms, generalizing previous results from [15] in Euclidean space. We show that a sequence of measures, associated to…

We establish the Gauss-Green formula for extended divergence-measure fields (i.e., vector-valued measures whose distributional divergences are Radon measures) over open sets. We prove that, for almost every open set, the normal trace is a…

In this paper, we prove existence and uniqueness of measure solutions for the Cauchy problem associated to the (vectorial) continuity equation with a non-local flow. We also give a stability result with respect to various parameters.

We consider the problem of uniform steady supersonic Euler flows passing a straight conical body with attack angles, and study Radon measure solutions describing the infinite-thin shock layers, particularly for the Chaplygin gas and…

We study nonnegative solutions of the Cauchy problem $$ \begin{cases} u_t+[\varphi(u)]_x=0 & \text{in } \mathbb{R}\times (0,T) \\ u=u_0\ge 0&\text{in } \mathbb{R}\times \{0\}, \end{cases} $$ where $u_0$ is a Radon measure and…

This paper is concerned with the large-time behavior of solutions to the Cauchy problem of the one-dimensional viscous radiative and reactive gas. Based on the elaborate energy estimates, we developed a new approach to derive the upper…

Cosmic rays (CRs) are frequently modeled as an additional fluid in hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations of astrophysical flows. The standard CR two-fluid model is described in terms of three conservation laws…

We consider the Cauchy problem in R^n for some types of damped wave equations. We derive asymptotic profiles of solutions with weighted L^{1,1}(R^n) initial data by employing a simple method introduced by the first author. The obtained…

In this paper, we study the Cauchy problem and multi-soliton solutions for a two-component short pulse system. For the Cauchy problem, we first prove the existence and uniqueness of solution with an estimate of the analytic lifespan, and…

In this paper, we obtain necessary conditions and sufficient conditions on the initial data for the local-in-time solvability of the Cauchy problem \[ \partial_t u +(-\Delta)^\frac{\theta}{2} u=|x|^{-\gamma} u^p ,\quad x\in{\bf R}^N, t>0,…

We consider a model for flow of liquid and gas in a pipe. We assume that the gas is ideal and that the liquid is incompressible. Under this assumption the resulting equations, expressing conservation of mass and momentum, splits into two…

We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures, and the solutions admit the concentration of mass. It is found that, under the requirement of satisfying the…

We analyze a class of weakly differentiable vector fields (\FF \colon \rn \to \rn) with the property that (\FF\in L^{\infty}) and (\div \FF) is a Radon measure. The primary focus of our investigation is to introduce a suitable notion of the…