Weak Solutions for a Fourth Order Degenerate Parabolic Equation
نویسندگان
چکیده
منابع مشابه
Solutions of a Fourth Order Degenerate Parabolic Equation with Weak Initial Trace
We show that the nonlinear fourth order degenerate parabolic equation u t + div (u n ru) = 0; n > 0 admits nonnegative solutions to initial data which are a nonnegative Radon measure provided that n < 2. In addition, we prove that the equation has a regularizing eeect in the sense that the solution we construct is in H 1 (R N) for all positive times and in H 2 loc (R N) for almost all positive ...
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By means of energy and entropy estimates, we prove existence and positivity results in higher space dimensions for degenerate parabolic equations of fourth order with nonnegative initial values. We discuss their asymptotic behaviour for t ! 1 and give a counterexample to uniqueness. 0. Introduction In this paper we will present new results on existence, (non)uniqueness, positivity and asymptoti...
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By means of energy and entropy estimates, we prove existence and positivity results in higher space dimensions for degenerate parabolic equations of fourth order with nonnegative initial values. We discuss their asymptotic behavior for t → ∞ and give a counterexample to uniqueness.
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A nonlinear parabolic equation of the fourth order is analyzed. The equation is characterized by a mobility coefficient that degenerates at 0. Existence of at least one weak solution is proved by using a regularization procedure and deducing suitable a-priori estimates. If a viscosity term is added and additional conditions on the nonlinear terms are assumed, then it is proved that any weak sol...
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We consider a fully practical nite element approximation of the fourth order nonlinear degenerate parabolic equation u t + r:(b(u)ru)= 0; where generically b(u) := juj p for any given p 2 (0; 1). An iterative scheme for solving the resulting nonlinear discrete system is analysed. In addition to showing well-posedness of our approximation, we prove convergence in one space dimension. Finally som...
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ژورنال
عنوان ژورنال: Bulletin of the Polish Academy of Sciences Mathematics
سال: 2006
ISSN: 0239-7269,1732-8985
DOI: 10.4064/ba54-1-3