Electron. J. Differential Equations, Vol. 2018 (2018), No. 198, pp. 1-8.

Nonexistence of nonnegative solutions for parabolic inequalities in the half-space

Evgeny I. Galakhov, Olga A. Salieva, Liudmila A. Uvarova

Based on the method of nonlinear capacity, we study the nonexistence of nonnegative monotonic solutions for the quasilinear parabolic inequality $u_t-\Delta_p u\ge u^q$. Also we study generalizations in the half-space in terms of parameters p and q.

Submitted March 22, 2018. Published December 12, 2018.
Math Subject Classifications: 35K92, 35R45.
Key Words: Quasilinear parabolic inequalities; monotonicity; nonexistence of solutions

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Evgeny I. Galakhov
RUDN University
ul. Miklukho-Maklaya, 6
Moscow 117198, Russia
email: galakhov@rambler.ru
Olga A. Salieva
MSTU "Stankin"
Vadkovsky per. 1
Moscow 127055, Russia
email: olga.a.salieva@gmail.com
Liudmila A. Uvarova
MSTU "Stankin"
Vadkovsky per. 1
Moscow 127055, Russia
email: uvar11@yandex.com

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