Shigesada-Kawasaki-Teramoto model on higher dimensional domains.
Some models of Cahn-Hilliard equations in nonisotropic media
Some models of Cahn-Hilliard equations in nonisotropic media
We derive in this article some models of Cahn-Hilliard equations in nonisotropic media. These models, based on constitutive equations introduced by Gurtin in [19], take the work of internal microforces and also the deformations of the material into account. We then study the existence and uniqueness of solutions and obtain the existence of finite dimensional attractors.
Some properties of solutions for a class of metaparabolic equations.
Stability and gradient dynamical systems.
The objective in these notes is to present an approach to dynamical systems in infinite dimensions. It does not seem reasonable to make a comparison of all of the orbits of the dynamics of two systems on non locally compact infinite dimensional spaces. Therefore, we choose to compare them on the set of globally defined bounded solutions. Fundamental problems are posed and several important results are stated when this set is compact. We then give results on the dynamical system which will ensure...
Stability and instability of equilibria on singular domains
We show existence of nonconstant stable equilibria for the Neumann reaction-diffusion problem on domains with fractures inside. We also show that the stability properties of all hyperbolic equilibria remain unchanged under domain perturbation in a quite general sense, covered by the theory of Mosco convergence.
Stationary radial solutions for a quasilinear Cahn-Hilliard model in space dimensions.
Strong global attractor for a quasilinear nonlocal wave equation on .