Admissible solutions for a class of nonlinear parabolic problems with non-negative data (Q2764658)
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scientific article; zbMATH DE number 1690778
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Admissible solutions for a class of nonlinear parabolic problems with non-negative data |
scientific article; zbMATH DE number 1690778 |
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Admissible solutions for a class of nonlinear parabolic problems with non-negative data (English)
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9 April 2002
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porous medium equation
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comparison principles
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viscosity solutions
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The authors introduce a new class of solutions for nonlinear parabolic equations similar to the porous medium equation. The idea is (loosely speaking) that these solutions satisfy the equation pointwise wherever they are positive and they are everywhere nonnegative. Such solutions obey a comparison principle which does not follow from the usual theory of viscosity solutions. On the other hand, they coincide with viscosity solutions provided the differential equation is proper in the following sense: The differential equation has the form NEWLINE\[NEWLINE u_t = F(x,t,u,Du,D^2 u) NEWLINE\]NEWLINE and \(F(x,t,z,p,r)\) is decreasing with respect to \(z\).
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