On some properties of solutions of quasilinear degenerate parabolic equations in
We study the asymptotic behaviour near infinity of the weak solutions of the Cauchy-problem.
On some sufficient conditions for the blow-up solutions of the nonlinear Ginzburg-Landau-Schrödinger evolution equation.
On stabilization and control for the critical Klein-Gordon equation on a 3-D compact manifold
We study the internal stabilization and control of the critical nonlinear Klein-Gordon equation on 3-D compact manifolds. Under a geometric assumption slightly stronger than the classical geometric control condition, we prove exponential decay for some solutions bounded in the energy space but small in a lower norm. The proof combines profile decomposition and microlocal arguments. This profile decomposition, analogous to the one of Bahouri-Gérard [2] on , is performed by taking care of possible...
On the accuracy of asymptotic approximations for longitudinal deformation of a thin plate
On the asymptotic behavior for convection-diffusion equations associated to higher order elliptic operators in divergence form.
We consider the linear convection-diffusion equation associated to higher order elliptic operators⎧ ut + Ltu = a∇u on Rnx(0,∞)⎩ u(0) = u0 ∈ L1(Rn),where a is a constant vector in Rn, m ∈ N*, n ≥ 1 and L0 belongs to a class of higher order elliptic operators in divergence form associated to non-smooth bounded measurable coefficients on Rn. The aim of this paper is to study the asymptotic behavior, in Lp (1 ≤ p ≤ ∞), of the derivatives Dγu(t) of the solution of the convection-diffusion equation...
On the asymptotic behavior of solutions of linear parabolic equations in space
On the asymptotic behavior of solutions of parabolic equations
On the asymptotic behavior of solutions of second order parabolic partial differential equations
We consider the second order parabolic partial differential equation . Sufficient conditions are given under which every solution of the above equation must decay or tend to infinity as |x|→ ∞. A sufficient condition is also given under which every solution of a system of the form , where , must decay as t → ∞.
On the asymptotic behavior of the motion of a viscous, heat-conducting, one-dimensional real gas.
On the asymptotics of solutions of elliptic equations in a neighborhood of a crack with nonsmooth front.
On the asymptotics of solutions to the second initial boundary value problem for Schrödinger systems in domains with conical points
In this paper, for the second initial boundary value problem for Schrödinger systems, we obtain a performance of generalized solutions in a neighborhood of conical points on the boundary of the base of infinite cylinders. The main result are asymptotic formulas for generalized solutions in case the associated spectrum problem has more than one eigenvalue in the strip considered.
On the Asypmptotic Behaviour of Solutions of Nonlinear Parabolic Equations.
On the behavior of a nonstationary Poiseuille solution as .
On the behaviour of generalized solutions to genuinely nonlinear first order equations for small and large values of time.
The paper deals with the asymptotic behavior of generalized solutions to nonlinear first order equations. With the aid of explicit variational representation one studies the decrease of solutions for a large time. And for the small time an asymptotic of the perturbation?s front is calculated.
On the behaviour of solutions to the nonlinear elliptic Neumann problem in unbounded domains
The asymptotic behaviour is studied for minima of regular variational problems with Neumann boundary conditions on noncompact part of boundary.
On the blow up phenomenon for the critical nonlinear Schrödinger equation in 1D
On the blowing up of solutions to nonlinear wave equations in two space dimensions.
On the blowup of multidimensional semilinear heat equations
On the blowup theory for the critical nonlinear Schrödinger equations
On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions