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
On the Caginalp system with dynamic boundary conditions and singular potentials
This article is devoted to the study of the Caginalp phase field system with dynamic boundary conditions and singular potentials. We first show that, for initial data in , the solutions are strictly separated from the singularities of the potential. This turns out to be our main argument in the proof of the existence and uniqueness of solutions. We then prove the existence of global attractors. In the last part of the article, we adapt well-known results concerning the Łojasiewicz inequality in...
On the complex structure of positive solutions to Matukuma-type equations
On the Convective Cahn-Hilliard Equation
The author studies the convective Cahn-Hilliard equation. Some results on the existence of classical solutions and asymptotic behavior of solutions are established. The instability of the traveling waves is also discussed.
On the decay estimates for the wave equation with a local degenerate or nondegenerate dissipation.
On the Decay of Solutions of Some Nonlinear Dissipative Wave Equations in Higher Dimensions.
On the dimension of the pullback attractors for -Navier-Stokes equations.