We consider a class of Kirchhoff type reaction-diffusion equations with variable exponents and source terms We prove with suitable assumptions on the variable exponents the global existence...
In this paper we study the Cahn-Hilliard-Gurtin system describing the phase-separation process in elastic solids. The system has been derived by Gurtin (1996) as an extension of the classical Cahn-Hilliard equation. For a version with viscosity we prove the existence and uniqueness of a weak solution on an infinite time interval and derive an absorbing set estimate.
We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and Debye-Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method due to S. Montgomery-Smith.
This paper considers a reaction-diffusion system with biatic diffusion.Existence of a globally bounded solution is proved and its large timebehaviour is given.
We consider the damped wave equation on the whole real line, where is a bistable potential. This equation has travelling front solutions of the form which describe a moving interface between two different steady states of the system, one of which being the global minimum of . We show that, if the initial data are sufficiently close to the profile of a front for large , the solution of the damped wave equation converges uniformly on to a travelling front as . The proof of this global stability...
In this paper we prove the existence of a global φ-attractor in the weak topology of the natural phase space for the family of multi-valued processes generated by solutions of a nonautonomous modified 3D Bénard system in unbounded domains for which Poincaré inequality takes place.