Blow up versus global boundedness of solutions of reaction diffusion equations with nonlinear boundary conditions
Extremal equilibria for parabolic non-linear reaction-diffusion equations
Dissipative dynamics of reaction diffusion equations in
Robin type conditions arising from concentrated potentials
Asymptotic behaviour for a phase field model in higher order Sobolev spaces.
In this paper we analyze the long time behavior of a phase-field model by showing the existence of global compact attractors in the strong norm of high order Sobolev spaces.
A note on the Cahn-Hilliard equation in involving critical exponent
We consider the Cahn-Hilliard equation in with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as and logistic type nonlinearities. In both situations we prove the -bound on the solutions and show that the individual solutions are suitably attracted by the set of equilibria. This complements the results in the literature; see J. W. Cholewa, A. Rodriguez-Bernal (2012).
Boundedness of global solutions for nonlinear parabolic equations involving gradient blow-up phenomena
We consider a one-dimensional semilinear parabolic equation with a gradient nonlinearity. We provide a complete classification of large time behavior of the classical solutions : either the space derivative blows up in finite time (with itself remaining bounded), or is global and converges in norm to the unique steady state. The main difficulty is to prove boundedness of all global solutions. To do so, we explicitly compute a nontrivial Lyapunov functional by carrying out the method of...
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