Some properties of solutions for an evolution \(p(x)\)-Laplacian equation

DOI10.1134/S1995080211010082zbMath1257.35114MaRDI QIDQ694388

Zhenbang Li, Honglei Lang, Chein-Shan Liu

Publication date: 12 December 2012

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

existenceuniquenessgeneralized Newtonian fluidstime-discrete method

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order parabolic equations (35K20) Weak solutions to PDEs (35D30) Quasilinear parabolic equations with (p)-Laplacian (35K92) Quasilinear parabolic equations (35K59)

Cites Work

• Unnamed Item
• Degenerate parabolic equations
• Orlicz spaces and modular spaces
• Strong solutions for generalized Newtonian fluids
• Global \(C^{1,\alpha}\) regularity for variable exponent elliptic equations in divergence form
• Regularity results for parabolic systems related to a class of non-Newtonian fluids.
• Regularity results for stationary electro-rheological fluids
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Existence and nonexistence of solutions for \(u_ t=\text{div}(|\nabla u|^{p-2}\nabla u)+f(\nabla u,u,x,t)\)
• Higher integrability for parabolic equations of \(p(x,t)\)-Laplacian type
• The interface blow-up phenomenon and local estimates for doubly degenerate parabolic equations
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

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