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

DOI10.1016/j.jmaa.2016.03.045zbMath1339.35060OpenAlexW2310410757MaRDI QIDQ269441

Lisa Santos, Fernando Miranda, Stanislav N. Antontsev

Publication date: 18 April 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.03.045

zbMATH Keywords

Galerkin's methodvariable exponents\(p(x, t)\)-curl systemsextinction in timestabilization towards zero

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with optics and electromagnetic theory (35Q60) Blow-up in context of PDEs (35B44)

Related Items (15)

Equivalent Relations with the J. L. Lions Lemma in a Variable Exponent Sobolev Space and Their Applications ⋮ Existence and multiplicity of solutions for \(p(x)\)-curl systems without the Ambrosetti-Rabinowitz condition ⋮ Properties of a quasi-uniformly monotone operator and its application to the electromagnetic \(p\)-curl systems. ⋮ Multiple solutions for p(x)${p(x)}$‐curl systems with nonlinear boundary condition ⋮ Existence of positive solutions and asymptotic behavior for evolutionary \(q(x)\)-Laplacian equations ⋮ On the \(p(x)\)-curl-system problem with indefinite weight and nonstandard growth conditions ⋮ Existence solution for curl-curl Kirchhoff problem ⋮ Existence and nonexistence of solutions for p(x)-curl systems arising in electromagnetism ⋮ Estimating the gradient of vector fields via div and curl in variable exponent Sobolev spaces ⋮ Multiple solutions to a class of electromagnetic \(p(x)\)-curl systems ⋮ Existence of two solutions for \(p(x)\)-curl systems with a small perturbation ⋮ Existence and multiplicity of solutions for \(p(x)\)-curl systems arising in electromagnetism ⋮ Existence of solutions for systems arising in electromagnetism ⋮ Eigenvalue problems for fractional \(p(x,y)\)-Laplacian equations with indefinite weight ⋮ Existence of solutions for a nonhomogeneous Dirichlet problem involving \(p(x)\)-Laplacian operator and indefinite weight

Cites Work

• A class of electromagnetic \(p\)-curl systems: blow-up and finite time extinction
• Lebesgue and Sobolev spaces with variable exponents
• Blow-up of solutions to parabolic equations with nonstandard growth conditions
• Vanishing solutions of anisotropic parabolic equations with variable nonlinearity
• Compact sets in the space \(L^ p(0,T;B)\)
• Elliptic partial differential equations of second order
• A CLASS OF STATIONARY NONLINEAR MAXWELL SYSTEMS
• Evolution PDEs with Nonstandard Growth Conditions

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