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
Journal ISSN
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.
Rights
Attribution 4.0 International