相关论文: Asymptotic Behavior of Solutions to a Model System…

We consider a periodic array of resonators, formed from Euler-Bernoulli beams, attached to the surface of an elastic half-space. Earlier studies of such systems have concentrated on compressional resonators. In this paper we consider the…

We study the asymptotic behavior of the principal eigenvalue of a weakly coupled, cooperative linear elliptic system in a stationary ergodic heterogeneous medium. The system arises as the so-called multigroup diffusion model for neutron…

We study the asymptotic behavior of blow-up solutions of the heat equation with nonlinear boundary conditions. In particular, we classify the asymptotic behavior of blow-up solutions and investigate the spacial singularity of their blow-up…

We study the radial relaxation dynamics toward equilibrium and time-periodic pulsating spherically symmetric gas bubbles in an incompressible liquid due to thermal effects. The asymptotic model ([A. Prosperetti, J. Fluid Mech., 1991] and…

We study the large-time behavior of solutions to the compressible Navier-Stokes equations for a viscous and heat-conducting ideal polytropic gas in the one-dimensional half-space. A rarefaction wave and its superposition with a…

In this paper, we deal with the following quasilinear elliptic system involving gradient terms in the form: \begin{center} $\begin{cases} \Delta_p u= v^m| \nabla u |^\alpha& \text{in}\quad \Omega\\ \Delta_p v= v^\beta| \nabla u |^q &…

In this paper, we observe how the heat equation in a non-cylindrical domain can arise as the asymptotic limit of a parabolic problem in a cylindrical domain, by adding a potential that vanishes outside the limit domain. This can be seen as…

We study the asymptotic behavior of solutions to the heat equation in nonhomogeneous media with critical singular density $$ |x|^{-2}\partial_{t}u=\Delta u, \quad \hbox{in} \ \real^N\times(0,\infty). $$ The asymptotic behavior proves to…

In this paper, we consider the energy decay of a damped hyperbolic system of wave-wave type which is coupled through the velocities. We are interested in the asymptotic properties of the solutions of this system in the case of indirect…

In these lecture notes, we address the problem of large-time asymptotic behaviour of the solutions to scalar convection-diffusion equations set in ${R}^N$. The large-time asymptotic behaviour of the solutions to many convection-diffusion…

We study local (the heat equation) and nonlocal (convolution type problems with an integrable kernel) evolution problems on a metric connected finite graph in which some of the edges have infinity length. We show that the asymptotic…

We study the asymptotics of solutions to a particular class of systems of linear wave equations, namely, of silent equations. We obtain asymptotic estimates of all orders for the solutions, and show that solutions are uniquely determined by…

In this work we consider a wide range of energy critical wave equation in 3-dimensional space with radial data. We are interested in exterior scattering phenomenon, in which the asymptotic behaviour of a solutions $u$ to the non-linear wave…

We consider in this contribution a simplified idealized one-dimensional model in a nuclear core reactor coupling the diffusion equation on the neutron flux withthe enthalpy equation for the water which collects the heat produced by this…

In this paper, we study the asymptotic behavior of radial solutions for several weighted elliptic equations with power type or exponential type nonlinearities on an annulus.

We consider a certain ultrahyperbolic equation in a Euclidean space being a generalization of Klein-Gordon-Fock equation. The behavior of solutions at points tending to infinity along timelike directions is studied. We examine the issue of…

In this paper we deal with the asymptotic behavior as $t$ tends to infinity of solutions for linear parabolic equations whose model is $$ \begin{cases} u_{t}-\Delta u = \mu & \text{in}\ (0,T)\times\Omega,\\[0.7 ex] u(0,x)=u_0 & \text{in}\…

We show that, on a complete, connected and non-compact Riemannian manifold of non-negative Ricci curvature, the solution to the heat equation with $L^{1}$ initial data behaves asymptotically as the mass times the heat kernel. In contrast to…

We study the ``hyperboloidal Cauchy problem'' for linear and semi-linear wave equations on Minkowski space-time, with initial data in weighted Sobolev spaces allowing singular behaviour at the boundary, or with polyhomogeneous initial data.…

The aim of this paper is to establish time decay properties and dispersive estimates for strictly hyperbolic equations with homogeneous symbols and with time-dependent coefficients whose derivatives are integrable. For this purpose, the…