On a class of nonlinear degenerate parabolic equations
On a conserved Penrose-Fife type system
We deal with a class of Penrose-Fife type phase field models for phase transitions, where the phase dynamics is ruled by a Cahn-Hilliard type equation. Suitable assumptions on the behaviour of the heat flux as the absolute temperature tends to zero and to are considered. An existence result is obtained by a double approximation procedure and compactness methods. Moreover, uniqueness and regularity results are proved as well.
On a critical threshold for nonlinear diffusion equations.
We study some aspects of the asymptotic behavior of the solutions to a class of nonlinear parabolic equations.
On a Decay Property of Weak Solution for Semilinear Evolution Equation of Parabolic Type and Its Applications.
On a method for solving a classical variational problem.
On a mixed problem for a linear coupled system with variable coefficients.
On a model of rotating superfluids
We consider an energy-functional describing rotating superfluids at a rotating velocity , and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical above which energy-minimizers have vortices, evaluations of the minimal energy as a function of , and the derivation of a limiting free-boundary problem.
On a model of rotating superfluids
We consider an energy-functional describing rotating superfluids at a rotating velocity ω, and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical ω above which energy-minimizers have vortices, evaluations of the minimal energy as a function of ω, and the derivation of a limiting free-boundary problem.
On a nonlinear coupled system with internal damping.
On a nonlinear wave equation with damping.
On a nonlocal eigenvalue problem
On a singular sublinear polyharmonic problem.
On admissibility for parabolic equations in ℝⁿ
We consider the parabolic equation (P) , (t,x) ∈ ℝ₊ × ℝⁿ, and the corresponding semiflow π in the phase space H¹. We give conditions on the nonlinearity F(x,u), ensuring that all bounded sets of H¹ are π-admissible in the sense of Rybakowski. If F(x,u) is asymptotically linear, under appropriate non-resonance conditions, we use Conley’s index theory to prove the existence of nontrivial equilibria of (P) and of heteroclinic trajectories joining some of these equilibria. The results obtained extend...
On an existence theorem for the Navier-Stokes equations with free slip boundary condition in exterior domain
This paper deals with a nonstationary problem for the Navier-Stokes equations with a free slip boundary condition in an exterior domain. We obtain a global in time unique solvability theorem and temporal asymptotic behavior of the global strong solution when the initial velocity is sufficiently small in the sense of Lⁿ (n is dimension). The proof is based on the contraction mapping principle with the aid of estimates for the Stokes semigroup associated with a linearized problem, which is also...
On an over-determined problem of free boundary of a degenerate parabolic equation
This work is concerned with the inverse problem of determining initial value of the Cauchy problem for a nonlinear diffusion process with an additional condition on free boundary. Considering the flow of water through a homogeneous isotropic rigid porous medium, we have such desire: for every given positive constants and , to decide the initial value such that the solution satisfies , where . In this paper, we first establish a priori estimate and a more precise Poincaré type inequality...
On anisotropic, dispersive and dissipative wave equations
On asymptotic behavior of global solutions for hyperbolic hemivariational inequalities.
On Asymptotic Behavior of Solution for the Navier-Stokes Equations in a Time Dependent Domain.
On asymptotic behavior of solutions of the Dirichlet problem in half-space for linear and quasi-linear elliptic equations.
On asymptotic behaviour of the dynamical systems generated by von Foerster-Lasota equations