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math.AP2008
A sharp estimate and change on the dimension of the attractor for Allen-Cahn equations
Nikos I. Karachalios, Nikos B. Zographopoulos
We consider the semilinear reaction diffusion equation , in a bounded domain . We assume the standard Allen-Cahn-type nonl…
math.AP2005
On the Dynamics of a Degenerate Parabolic Equation: Global Bifurcation of Stationary States and Convergence
Nikos I. Karachalios, Nikos B. Zographopoulos
We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points or be unbounded. We show the e…