TITLE

On the dynamics of a degenerate parabolic equation: global bifurcation of stationary states and convergence

AUTHOR(S)
Karachalios, Nikos; Zographopoulos, Nikos
PUB. DATE
March 2006
SOURCE
Calculus of Variations & Partial Differential Equations;Mar2006, Vol. 25 Issue 3, p361
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
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 existence of a global branch of nonnegative stationary states, covering both the cases of a bounded and an unbounded domain. The global bifurcation of stationary states, implies-in conjuction with the definition of a gradient dynamical system in the natural phase space-that at least in the case of a bounded domain, any solution with nonnegative initial data tends to the trivial or the nonnegative equilibrium. Applications of the global bifurcation result to general degenerate semilinear as well as to quasilinear elliptic equations, are also discussed.
ACCESSION #
19870395

 

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