Page 1

Displaying 1 – 6 of 6

Showing per page

Bistable traveling waves for monotone semiflows with applications

Jian Fang, Xiao-Qiang Zhao (2015)

Journal of the European Mathematical Society

This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. In an abstract setting, we establish the existence of traveling waves for discrete and continuous-time monotone semiflows in homogeneous and periodic habitats. The results are then extended to monotone semiflows with weak compactness. We also apply the theory to four classes of evolution systems.

Existence results for a fourth order partial differential equation arising in condensed matter physics

Carlos Escudero, Filippo Gazzola, Robert Hakl, Ireneo Peral, Pedro José Torres (2015)

Mathematica Bohemica

We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation which nonlinearity is the determinant of the Hessian matrix of the solution. We consider this model in a bounded domain of the real plane and study its stationary solutions both when the geometry of this domain is arbitrary and when it is the unit ball and the solution is radially symmetric. We also consider the initial-boundary value problem...

Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations

Thomas Bartsch, Peter Poláčik, Pavol Quittner (2011)

Journal of the European Mathematical Society

We prove a Liouville type theorem for sign-changing radial solutions of a subcritical semilinear heat equation u t = Δ u + u p - 1 u . We use this theorem to derive a priori bounds, decay estimates, and initial and final blow-up rates for radial solutions of rather general semilinear parabolic equations whose nonlinearities have a subcritical polynomial growth. Further consequences on the existence of steady states and time-periodic solutions are also shown.

On a phase-field model with a logarithmic nonlinearity

Alain Miranville (2012)

Applications of Mathematics

Our aim in this paper is to study the existence of solutions to a phase-field system based on the Maxwell-Cattaneo heat conduction law, with a logarithmic nonlinearity. In particular, we prove, in one and two space dimensions, the existence of a solution which is separated from the singularities of the nonlinear term.

Spreading and vanishing in nonlinear diffusion problems with free boundaries

Yihong Du, Bendong Lou (2015)

Journal of the European Mathematical Society

We study nonlinear diffusion problems of the form u t = u x x + f ( u ) with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For special f ( u ) of the Fisher-KPP type, the problem was investigated by Du and Lin [DL]. Here we consider much more general nonlinear terms. For any f ( u ) which is C 1 and satisfies f ( 0 ) = 0 , we show that the omega limit set ω ( u ) of every bounded positive solution is determined by a stationary solution....

Currently displaying 1 – 6 of 6

Page 1