Decay estimates for solutions of various parabolic problems (Q2712993)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Decay estimates for solutions of various parabolic problems |
scientific article |
Statements
4 March 2002
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maximum principles for derived functions
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Decay estimates for solutions of various parabolic problems (English)
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The authors consider problems of the form NEWLINE\[NEWLINEg(u, u^2_x) u_{xx}+ f(u)= u_t,\quad|x|< L,\quad t>0,NEWLINE\]NEWLINE where \(g\) has the form \(r(u)\cdot q(u^2_x)\) or \(r(u)+ q(u^2_x)\). They prove maximum principles for the expression \(\Phi(x, t)= \psi(u, u^2_x) e^{2\alpha\beta t}\) which in turn leads to decay bounds for \(u(x,t)\).
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