相关论文: Concentration in flux-function limits of solutions…
In this paper, we study the limiting behavior of Riemann solutions to the Euler equations of one-dimensional compressible fluid flow as $\gamma$ tends to one. We show that the limit solution forms the delta wave to the pressureless Euler…
In this paper, two kinds of occurrence mechanism on the phenomenon of concentration and the formation of delta shock waves are analyzed and identified in the flux approximation limit of Riemann solutions to the extended Chaplygin gas…
In this paper, we study the phenomenon of concentration and the formation of delta shock wave in vanishing adiabatic exponent limit of Riemann solutions to the Aw-Rascle traffic model. It is proved that as the adiabatic exponent vanishes,…
In this paper, we study the limits of Riemann solutions to the inhomogeneous Euler equations of one-dimensional compressible fluid flow as the adiabatic exponent $\gamma$ tends to one. Different from the homogeneous equations, the Riemann…
By the flux-approximation method, we study limits of Riemann solutions to the Brio system with two independent parameters. The Riemann problem of the perturbed system is solved analytically, and four kinds of solutions are obtained…
We consider a parabolic-ODE-parabolic chemotaxis system with radially symmetric initial data in a two-dimensional disk under the $0$-Neumann boundary condition. Although our system shares similar mathematical structures as the Keller--Segel…
In this paper, firstly, by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation, we construct parameterized delta-shock and constant density solutions, then we show that, as the flux perturbation…
The aim of this article is to study the limiting behavior of the solutions for the scaled generalized Euler equations of compressible fluid flow. When the initial data is of Riemann type, we showed the existence of solution which consists…
In this note we present some results concerning the concentration of sequences of first eigenfunctions on the limit sets of a Morse-Smale dynamical system on a compact Riemanniann manifold. More precisely a renormalized sequence of…
We consider the following singularly perturbed Neumann problem \begin{eqnarray*} \ve^2 \Delta u -u +u^p = 0 \, \quad u>0 \quad {\mbox {in}} \quad \Omega, \quad {\partial u \over \partial \nu}=0 \quad {\mbox {on}} \quad \partial \Omega,…
The notion of a delta shock wave and a singular shock wave was introduced and employed by different authors, and it was shown that a large class of Riemann problems can be solved globally with these additional building blocks. The aim of…
Two-phase solutions of focusing NLS equation are classically constructed out of an appropriate Riemann surface of genus two, and expressed in terms of the corresponding theta-function. We show here that in a certain limiting regime such…
Existence and admissibility of $\delta$-shock type solution is discussed for the following nonconvex strictly hyperbolic system arising in studues of plasmas: \pa_t u + \pa_x \big(\Sfrac{u^2+v^2}{2} \big) &=0 \pa_t v +\pa_x(v(u-1))&=0. The…
We consider the equation $-\epsilon^{2}\Delta u + u = u^ {p}$ in a bounded domain $\Omega\subset\R^{3}$ with edges. We impose Neumann boundary conditions, assuming $1<p<5$, and prove concentration of solutions at suitable points of…
We consider mass concentration properties of Laplace eigenfunctions $\varphi_\lambda$, that is, smooth functions satisfying the equation $-\Delta \varphi_\lambda = \lambda \varphi_\lambda$, on a smooth closed Riemannian manifold. Using a…
We consider a system of two conservation laws and provide a detailed description of both classical and non-classical self-similar Riemann solutions. In particular, we demonstrate the existence of overcompressive delta shocks as singular…
This paper concerns the concentration of Dirichlet eigenfunctions of the Laplacian on a compact two-dimensional Riemannian manifold with strictly geodesically concave boundary. We link three inequalities which bound the concentration in…
We consider the PDE flow associated to Riemann zeta and general Dirichlet $L$-functions. These are models characterized by nonlinearities appearing in classical number theory problems, and generalizing the classical holomorphic Riemann flow…
In this paper the local singularities of integrable Hamiltonian systems with two degrees of freedom are studied. The topological obstruction to the existence of focus-focus singularity with given complexity was found. It has been showed…
We consider a system consisting of one conservation law and one balance law with a time-dependent source term, and provide a comprehensive analysis of Riemann solutions, including the non-classical overcompressive delta shocks. The minimal…