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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 16
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Articles

Extinction of solutions in parabolic equations with different diffusion operators

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Pages 3600-3612 | Received 16 Nov 2019, Accepted 26 Jan 2020, Published online: 05 Feb 2020
 

ABSTRACT

In this paper, we study the evolution p, q-Laplacian equations ut=div(|u|p2u)+uαΩvmdx and vt=div(|v|q2v)+vβΩundx with 1<p, q<2, subject to homogeneous Dirichlet boundary conditions. If mn>(p1α)(q1β), there exist suitable initial data such that vanishing solutions exist. If mn<(p1α)(q1β), we find the explicit scopes of initial data such that the solutions could not vanish, which complete the corresponding classifications of solutions in Math. Methods Appl. Sci. 39 (2016) 1325–1335 and Appl. Math. Comp. 259 (2015) 587–595, respectively. For the critical case mn=(p1α)(q1β), the solutions vanish in finite time with small initial data.

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Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper is Shandong Provincial Natural Science Foundation of China.

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