Observations on Blow Up and Dead Cores for Nonlinear Parabolic Equations.
On a boundary value problem for an equation of the type of non-stationary filtration
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 method for solving a classical variational problem.
On a necessary and sufficient condition for a blowing up of a solution to a mixed boundary problem for a certain nonlinear equation of Sobolev type.
On a parabolic problem with nonlinear Newton boundary conditions
The paper is concerned with the study of a parabolic initial-boundary value problem with nonlinear Newton boundary condition considered in a two-dimensional domain. The goal is to prove the existence and uniqueness of a weak solution to the problem in the case when the nonlinearity in the Newton boundary condition does not satisfy any monotonicity condition and to analyze the finite element approximation.
On a Solution of Degenerate Elliptic-parabolic Systems in Orlicz-Sobolev Spaces II.
On a Solution of Degenerate Elliptic-parabolic Systems in Orlicz-Sobolev Spaces I.
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 approximate solution for quasilinear parabolic equations
On an evolution equation in Banach spaces
On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions
We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions tend to zero or blow up in a finite time. We also give the asymptotic behavior of solutions which tend to zero as . Finally, we obtain the asymptotic behavior near the blow-up time of certain blow-up solutions and describe their blow-up set.
On connecting orbits of semilinear parabolic equations on .
On contact problems for nonlinear parabolic functional differential equations.
On critical exponents for a system of heat equations coupled in the boundary conditions.
On critical exponents for the heat equation with a nonlinear boundary condition
On Galerkin approximations of parabolic equations in time dependent domains
On global existence and stationary solutions for two classes of semilinear parabolic problems
We investigate stationary solutions and asymptotic behaviour of solutions of two boundary value problems for semilinear parabolic equations. These equations involve both blow up and damping terms and they were studied by several authors. Our main goal is to fill some gaps in these studies.
On -convergence of Rothe’s method
On parabolic initial-boundary value problems with critical growth for the gradient