相关论文: Asymptotic integration and dispersion for hyperbol…

In this paper, we extend the results of [1] by proving exponential asymptotic $H^1$-convergence of solutions to a one-dimensional singular heat equation with $L^2$-source term that describe evolution of viscous thin liquid sheets while…

This letter is devoted to results on intermediate asymptotics for the heat equation. We study the convergence towards a stationary solution in self-similar variables. By assuming the equality of some moments of the initial data and of the…

We consider a nonlinear model for electrical conduction in biological tissues. The nonlinearity appears in the interface condition prescribed on the cell membrane. The purpose of this paper is proving asymptotic convergence for large times…

In this paper, we investigate the long-time asymptotic behavior of the solution to the initial value problem for the modified Camassa-Holm (mCH) equation with cubic nonlinearity. The equation is known to be integrable, which we mean it…

This paper is concerned with integral representations and asymptotic expansions of solutions to the time-periodic incompressible Navier-Stokes equations for fluid flow in the exterior of a rigid body that moves with constant velocity. Using…

The self-similar asymptotics for solutions to the drift-diffusion equation with fractional dissipation, coupled to the Poisson equation, is analyzed in the whole space. It is shown that in the subcritical and supercritical cases, the…

We investigate the large-time behavior of three types of initial-boundary value problems for Hamilton-Jacobi Equations with nonconvex Hamiltonians. We consider the Neumann or oblique boundary condition, the state constraint boundary…

We study the long-time asymptotic behavior of solutions u of the Hamilton-Jacobi equation u_t(x,t)+H(x,Du(x,t))=0 in \Omega \times (0,\infty), where \Omega is a bounded open subset of R^n, with Hamiltonian H=H(x,p) being convex and coercive…

This paper deals with the application of probabilistic time integration methods to semi-explicit partial differential-algebraic equations of parabolic type and its semi-discrete counterparts, namely semi-explicit differential-algebraic…

We study BV solutions for a $2\times2$ system of hyperbolic balance laws. We show that when initial data have small total variation on $(-\infty,\infty)$ and small amplitude, and decay sufficiently fast to a constant equilibrium state as…

For two linear evolution differential equations systems - a normal ordinary differential equations system and a partial differential equations system with Stokes operator in a main part - with rapidly oscillating by time coefficients in a…

We consider the so-called \emph{discrete $p$-Laplacian}, a nonlinear difference operator that acts on functions defined on the nodes of a possibly infinite graph. We study the associated nonlinear Cauchy problem and identify the generator…

We discuss solution concepts for linear hyperbolic equations with coefficients of regularity below Lipschitz continuity. Thereby our focus is on theories which are based either on a generalization of the method of characteristics or on…

We derive a Riemann--Hilbert representation for the solution of an integrable nonlinear evolution equation with a $3 \times 3$ Lax pair. We use the derived representation to obtain formulas for the long-time asymptotics.

In order to describe the dynamics of monochromatic surface waves in deep water, we derive a nonlinear and dispersive system of equations for the free surface elevation and the free surface velocity from the Euler equations in infinite…

We consider wave equations with a special type of log-fractional damping. We study the Cauchy problem for this model in the whole space, and we obtain an asymptotic profile and optimal estimates of solutions as time goes to infinity in…

We analyze the long-time asymptotics for the Degasperis--Procesi equation on the half-line. By applying nonlinear steepest descent techniques to an associated $3 \times 3$-matrix valued Riemann--Hilbert problem, we find an explicit formula…

This paper is concerned with space-time homogenization problems for damped wave equations with spatially periodic oscillating elliptic coefficients and temporally (arithmetic) quasi-periodic oscillating viscosity coefficients. Main results…

We discuss the well-posedness and decay of Besicovitch almost periodic solutions for a class of nonlinear degenerate anisotropic hyperbolic-parabolic equations. In our definition of weak entropy solution the initial data is only assumed in…

We consider large time asymptotics for damped nonlinear Schr\"{o}dinger equations. It is known that the nonlinear solution asymptotically behaves like a linear solution when time $t$ tends to infinity in the energy space. We prove that its…