相关论文: Dispersion and asymptotic profiles for Kirchhoff e…

In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.

We review the theory of modulation equations or Whitham equations for the travelling wave solution of KdV. We then apply the Whitham modulation equations to describe the long-time asymptotics and small dispersion asymptotics of the KdV…

Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…

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…

An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…

In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation (nonlocal mKdV) \[q_t(x,t)+q_{xxx}(x,t)-6q(x,t)q(-x,-t)q_x(x,t)=0,\] which can be viewed as a generalization of the…

An asymptotic small parameter expansion of a single Cauchy problem is constructed for a singularly perturbed system of hyperbolic equations describing vibrations of two rigidly connected strings. Equations (such as generalized Korteweg-de…

The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…

This paper is concerned with asymptotic persistence, extinction and spreading properties for non-cooperative Fisher-KPP systems with space-time periodic coefficients. Results are formulated in terms of a family of generalized principal…

We compute some asymptotic limits for solutions of Burgers equation with Cauchy data in $L^1(R)$.

We consider the long-time behavior of the massless Dirac equation coupled to a Coulomb potential. For nice enough initial data, we find a joint asymptotic expansion for solutions near the null and future infinities and characterize…

This work investigates the long-time asymptotic behaviors of the solution to the KdV equation with delta function initial profiles in different regions, employing the Riemann-Hilbert formulation and Deift-Zhou nonlinear steepest descent…

We establish new asymptotic results for the solutions of the second-grade fluids equations and characterize their decay rate in terms of the behavior of the initial data. Moreover, assuming more regularity for the initial data, we study the…

We establish the decay of the solutions of the damped wave equations in one dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions where the damping coefficient is a function of space and time. The analysis is based…

We study the time-asymptotic behavior of solutions of the Schr\"odinger equation with nonlinear dissipation \begin{equation*} \partial _t u = i \Delta u + \lambda |u|^\alpha u \end{equation*} in ${\mathbb R}^N $, $N\geq1$, where $\lambda\in…

We consider the propagation of acoustic time-harmonic waves in a homogeneous media containing periodic lattices of spherical or cylindrical inclusions. It is assumed that the wavelength has the order of the periods of the lattice while the…

We show that computing the coefficients of the Taylor expansion of the solution of the off-equilibrium dynamical equations characterizing models with quenched disorder is a very effective way to understand the long time asymptotic behavior.…

This paper is concerned with a quantitative analysis of asymptotic behaviors of (possibly sign-changing) solutions to the Cauchy-Dirichlet problem for the fast diffusion equation posed on bounded domains with Sobolev subcritical exponents.…

This paper reports on a new algorithm to compute the asymptotic solutions of a linear differential system. A feature of the algorithm is the ability to accommodate periodic coefficients.