相关论文: Higher order time asymptotics of fast diffusion in…

In this paper we present a formal analysis of the long-time asymptotics of a particular class of solutions of the Boltzmann equation, known as homoenergetic solutions, which have the form $f\left( x,v,t\right)=g\left( v-L\left( t\right)…

We present a new solver for nonlinear parabolic problems that is L-stable and achieves high order accuracy in space and time. The solver is built by first constructing a single-dimensional heat equation solver that uses fast O(N)…

We study metastable behavior in a discrete nonlinear Schr\"odinger equation from the viewpoint of Hamiltonian systems theory. When there are $n < \infty$ sites in this equation, we consider initial conditions in which almost all the energy…

We study some properties of a multi-species degenerate Ginzburg-Landau energy and its relation to a cross-diffusion Cahn-Hilliard system. The model is motivated by multicomponent mixtures where crossdiffusion effects between the different…

We consider the initial value problem for the viscous Fornberg-Whitham equation which is one of the nonlinear and nonlocal dispersive-dissipative equations. In this paper, we establish the global existence of the solutions and study its…

This paper continues the investigation of Du and Lou (J. European Math Soc, to appear), where the long-time behavior of positive solutions to a nonlinear diffusion equation of the form $u_t=u_{xx}+f(u)$ for $x$ over a varying interval…

We study the large-time behaviour of the solutions of the evolution equation involving nonlinear diffusion and gradient absorption, $$ \partial_t u - \Delta_p u + |\nabla u|^q=0 . $$ We consider the problem posed for $x\in \real^N$ and t>0…

We study the following nonlocal diffusion equation in the Heisenberg group $\mathbb{H}_n$, \[ u_t(z,s,t)=J\ast u(z,s,t)-u(z,s,t), \] where $\ast$ denote convolution product and $J$ satisfies appropriated hypothesis. For the Cauchy problem…

This paper is concerned with parabolic gradient systems of the form \[ u_t = -\nabla V(u) + \Delta_x u \,, \] where the space variable $x$ and the state variable $u$ are multidimensional, and the potential $V$ is coercive at infinity. For…

We investigate an asymptotic expansion of the solution of the master equation under the modulation of control parameters. In this case, the non-decaying part of the solution becomes the dynamical steady state expressed as an infinite series…

We construct a class of infinite mass functions for which solutions of the viscous Burgers equation decay at a better rate than solution of the heat equation for initial data in this class. In other words, we show an enhanced dissipation…

The long-time asymptotic behavior of the focusing nonlinear Schr\"odinger (NLS) equation on the line with symmetric nonzero boundary conditions at infinity is characterized by using the recently developed inverse scattering transform (IST)…

We consider the Cauchy problem for doubly nonlinear degenerate parabolic equations with inhomogeneous density on noncompact Riemannian manifolds. We give a qualitative classification of the behavior of the solutions of the problem depending…

We investigate the structures of the near-plate velocity and temperature profiles at different horizontal positions along the conducting bottom (and top) plate of a Rayleigh-B\'{e}nard convection cell, using two-dimensional (2D) numerical…

In this work, we generalize Sacks-Uhlenbeck's existence result for harmonic spheres, constructing for $n \ge 2$, regular, non-trivial, $n$-harmonic $n$-spheres into suitable target manifolds. We obtain an infinite family of new…

We consider an abstract second order evolution equation with damping. The "elastic" term is represented by a self-adjoint nonnegative operator A with discrete spectrum, and the nonlinear term has order greater than one at the origin. We…

We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of…

The emergence of non-configurational symmetry is studied in a minimal example. The system under scrutiny consists of a dimeric hexagonal complex with configurational $C_3$ symmetry, formulated as a tight-binding model. An accidental…

An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media…

The invariance for the equation of fast diffusion in the 2D coordinate space has been proved, and its reduction to the 1D (with respect to the spatial variable) analog is demonstrated. On the basis of these results, new exact…