相关论文: A singular limit problem for the Ibragimov-Shabat …
We consider the Rosenau equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solution of the Burgers equation.…
We consider the Rosenau-Korteweg-de Vries-equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solution of the dispersive equation converge to the discontinous weak solutions of…
We consider the regularized short-pulse equation, which contains nonlinear dis- persive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of…
We consider the Ostrovsky equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tend to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the…
We consider the Kudryashov-Sinelshchikov equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation coverge to the entropy ones of the Burgers…
We consider the Rosenau-Korteweg-de Vries-regularized long wave and Rosenau- Korteweg-de Vries equations, which contain nonlinear dispersive effects. We prove that, as the diffusion parameter tends to zero, the solutions of the dispersive…
We consider solutions of hyperbolic conservation laws regularized with vanishing diffusion and dispersion terms. Following a pioneering work by Schonbek, we establish the convergence of the regularized solutions toward discontinuous…
We study the convergence of solutions of the discrete nonlinear Klein-Gordon equation on an infinite lattice in the continuum limit, using recent tools developed in the context of nonlinear discrete dispersive equations. Our approach relies…
We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of…
We consider the dispersion managed nonlinear Schr\"odinger equation with power-law nonlinearity and its discrete version of equations with step size $h\in(0,1]$. We prove that the solutions of the discrete equations strongly converge in…
We introduce a dispersion approximation of weak, entropy solutions of multidimensional scalar conservation laws using variational kinetic representation, where equilibrium densities satisfy the Gibb's entropy minimization principle for a…
We consider a class of multidimensional conservation laws with vanishing nonlinear diffusion and dispersion terms. Under a condition on the relative size of the diffusion and dispersion coefficients, we establish that the…
In this article, we prove that small localized data yield solutions to Kawahara type equation which have linear dispersive decay on a finite time. We use the similar method used to derive the dispersive decay bound of the solutions to the…
The main purpose here is the study of dispersive blow-up for solutions of the Zakharov-Kuznetsov equation. Dispersive blow-up refers to point singularities due to the focusing of short or long waves. We will construct initial data such that…
Motivated by porous medium equations with randomly perturbed velocity field, this paper considers a class of nonlinear degenerate diffusion equations with nonlinear conservative noise in bounded domains. The existence, uniqueness and…
We consider the drift-diffusion equation $u_t-\epsilon\Delta u + \nabla \cdot(u\nabla K^*u)=0$ in the whole space with global-in-time solutions bounded in all Sobolev spaces; for simplicity, we restrict ourselves to the model case…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
In this paper, the existence, uniqueness and dependence on initial value of solution for a singular diffusion equation with nonlinear boundary condition are discussed. It is proved that there exists a unique global smooth solution which…
It is proved that the solutions to the singular stochastic $p$-Laplace equation, $p\in (1,2)$ and the solutions to the stochastic fast diffusion equation with nonlinearity parameter $r\in (0,1)$ on a bounded open domain $\Lambda\subset\R^d$…
We derive a diffusion approximation for the kinetic Vlasov-Fokker-Planck equation in bounded spatial domains with specular reflection type boundary conditions. The method of proof involves the construction of a particular class of test…