On the definition of viscosity solutions for parabolic equations (Q2723485)
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scientific article; zbMATH DE number 1614755
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the definition of viscosity solutions for parabolic equations |
scientific article; zbMATH DE number 1614755 |
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On the definition of viscosity solutions for parabolic equations (English)
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5 July 2001
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fully nonlinear equations
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\(p\)-parabolic equation
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In this paper, a refinement for the definition of the viscosity solution for the second-order parabolic equation \(u_t+ F(x,t,u,Du,D^2u)=0\) is given. The new version of the definition is equivalent to the usual one and it better adapts to the properties of parabolic equations. The basic idea is to determine the admissibility of a test function based on its behaviour prior to the given moment of time and ignore what happens at times after that.NEWLINENEWLINENEWLINETo demonstrate that the new definition makes the use of viscosity solutions more flexible, the author presents -- in the last section of this paper -- an application concerning the asymptotic behavior of the solutions of the so-called \(p\)-parabolic equation. In the proof, the new version of the definition of viscosity solutions is utilized in an essential way.
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