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Higher order nonlinear degenerate parabolic equations. (English) Zbl 0702.35143
The paper deals with a few existence and positivity results for higher order, possibly degenerate, nonlinear parabolic equations. The equations under investigation are of the type \[ \frac{du}{dt}+\frac{\partial}{\partial \kappa}(f(u)\frac{\partial^{2m+1}u}{\partial \kappa^{2m+1}})=0 \] where \(f(u)=| u|^ m\) \(f_ 0(u)\) with \(n\geq 1\) and \(f_ 0(u)>0.\)
Existence of a weak solution is shown for \(m\geq 2\). Furthermore if the initial data is nonnegative, the solution is also nonnegative. For \(n\geq 4\), the authors show that the support of the solution u increases with time t (a weaker form of this property being proved for \(2\leq n<4)\).
Reviewer: D.Blanchard

35K65 Degenerate parabolic equations
35K55 Nonlinear parabolic equations
35K25 Higher-order parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
Full Text: DOI
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