Blow-up and finite time extinction for p(x, t)-curl systems arising in electromagnetism

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:440

Article

Antontsev, Stanislav^1,2  Miranda, Fernando^3,4  Santos, Lisa^3,4 

[1] Univ Nova Lisboa, CMAF CIO, P-1200 Lisbon, Portugal

[2] Novosibirsk State Univ, Novosibirsk, Russia

[3] Univ Minho, CMAT, P-4719 Braga, Portugal

[4] Univ Minho, Dept Matemat & Aplicacoes, P-4719 Braga, Portugal

关键词: Electromagnetic problems;    p(x, t)-curl systems;    Variable exponents;    Blow-up;    Extinction in time;   

DOI  :  10.1016/j.jmaa.2016.03.045

来源: Elsevier

【 摘 要 】

We study a class of p(x, t)-curl systems arising in electromagnetism, with a nonlinear source term. Denoting by h the magnetic field, the source term considered is of the form lambda h (integral(Omega) vertical bar h vertical bar(2))(sigma-2/2) where lambda is an element of {-1, 0, 1}: when lambda is an element of {-1, 0} we consider 0 < sigma <= 2 and for lambda = 1 we have sigma >= 1. We introduce a suitable functional framework and a convenient basis that allow us to apply the Galerkin's method and prove existence of local or global solutions, depending on the values of lambda and sigma. We study the finite time extinction or the stabilization towards zero of the solutions when lambda is an element of {-1, 0} and the blow-up of local solutions when lambda = 1. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free