Nonexistence of global solutions to the system of semilinear parabolic equations with biharmonic operator and singular potential

Date

2018-01-06

Authors

Bagirov, Shirmayil

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In the domain Q′R = {x : |x| > R} x (0, +∞) we consider the problem ∂u1/∂t + ∆2u1 - C1/|x|4 u1 = |x|σ1|u2|q1, u1|t=0 = u1 0(x) ≥ 0, ∂u2/∂t + ∆2u2 - C2/|x|4 u2 = |x|σ2|u1|q2, u2|t=0 = u2 0(x) ≥ 0, ∫∞0 ∫∂BR ui ds dt ≥ 0, ∫∞0 ∫∂BR ∆ui ds dt ≤ 0, where σi ∈ ℝ, qi > 1, 0 ≤ Ci < (n(n-4)/4)2, i = 1, 2. Sufficient condition for the nonexistence of global solutions is obtained. The proof is based on the method of test functions.

Description

Keywords

System of semilinear parabolic equation, Biharmonic operator, Global solution, Critical exponent, Method of test functions

Citation

Bagirov, S. (2018). Nonexistence of global solutions to the system of semilinear parabolic equations with biharmonic operator and singular potential. <i>Electronic Journal of Differential Equations, 2018</i>(09), pp. 1-13.

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Attribution 4.0 International

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