Expansion of positivity to a class of doubly nonlinear parabolic equations
We establish the expansion of positivity of the nonnegative, local, weak solutions to the class of doubly nonlinear parabolic equations $$\partial_t (u^{q}) -\operatorname{div}{(|D u|^{p-2} D u)}=0, \qquad\ p>1 \ \text{and} \ q>0$$ considering separately the two possible cases $q+1-p > 0...
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| Format: | Article |
| Language: | English |
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University of Szeged
2022-04-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9283 |
| Summary: | We establish the expansion of positivity of the nonnegative, local, weak solutions to the class of doubly nonlinear parabolic equations
$$\partial_t (u^{q}) -\operatorname{div}{(|D u|^{p-2} D u)}=0, \qquad\ p>1 \ \text{and} \ q>0$$
considering separately the two possible cases $q+1-p > 0$ and $q+1-p<0$. The proof relies on the procedure presented by DiBenedetto, Gianazza and Vespri for both the degenerate and the singular parabolic $p$-Laplacian equation. |
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| ISSN: | 1417-3875 |