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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

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