Geodesic
Some nonexistence results for higher-order evolution inequalities in cone-like domains
Laptev, Gennady1
1 Department of Function Theory, Steklov Mathematical Institute, Gubkina Street 8, Moscow, Russia
Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 87-93.

Voir la notice de l'article provenant de la source American Mathematical Society

Nonexistence of global (positive) solutions of semilinear higher-order evolution inequalities \begin{equation*} \frac {\partial ^k u}{\partial t^k}-\Delta u^m\ge |u|^q,\quad \frac {\partial ^k u}{\partial t^k}-\Delta u\ge |x|^\sigma u^q,\quad \frac {\partial ^ku}{\partial t^k}-\operatorname{div} (|x|^\alpha Du)\ge u^q \end{equation*} with $k=1,2,\dots$, in cone-like domains is studied. The critical exponents $q^*$ are found and the nonexistence results are proved for $1$. Remark that the corresponding result for $k=1$ (parabolic problem) is sharp.
DOI : 10.1090/S1079-6762-01-00098-1

Laptev, Gennady 1

1 Department of Function Theory, Steklov Mathematical Institute, Gubkina Street 8, Moscow, Russia 
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Laptev, Gennady. Some nonexistence results for higher-order evolution inequalities in cone-like domains. Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 87-93. doi : 10.1090/S1079-6762-01-00098-1. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-01-00098-1/

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