Uniqueness of solutions of the parabolic variational inequality with variable exponent of nonlinearity

DOI10.1016/j.na.2008.03.013zbMath1162.35399OpenAlexW2082184466MaRDI QIDQ1004631

O. M. Buhrii, Rabil Ayazoglu (Mashiyev)

Publication date: 11 March 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.03.013

zbMATH Keywords

variable exponent Lebesgue and Sobolev spacesnonlinear parabolic variational inequality

Mathematics Subject Classification ID

Variational inequalities (49J40) Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators (35K85)

Related Items (14)

Variational analysis for an indefinite quasilinear problem with variable exponent ⋮ Integro-differential systems with variable exponents of nonlinearity ⋮ Existence of solutions of the parabolic variational inequality with variable exponent of nonlinearity ⋮ Unnamed Item ⋮ Existence of solutions for a class of elliptic systems in \(\mathbb R^{N}\) involving the \((p(x),q(x))\)-Laplacian ⋮ The unique solvability of a problem without initial conditions for linear and nonlinear elliptic-parabolic equations ⋮ The existence of weak solutions for parabolic variational inequalities with(p(x,t), q(x,t))-growth ⋮ On the existence of mild solutions of the initial-boundary-value problems for the Petrovskii-type semilinear parabolic systems with variable exponents of nonlinearity ⋮ Hyperbolic variational inequality of the third order with variable exponent of nonlinearity ⋮ Lyapunov, Opial and Beesack inequalities for one-dimensional \(p(t)\)-Laplacian equations ⋮ Existence of solutions for parabolic equations of Kirchhoff type involving variable exponent ⋮ Doubly nonlinear parabolic equations with variable exponents of nonlinearity ⋮ Unnamed Item ⋮ Existence of solution for an indefinite weight quasilinear problem with variable exponent

Cites Work

• A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions
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• Some properties of variable Sobolev capacity
• Topology of the space \(\mathcal L^{p(t)}([0,t)\)]
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• ON PASSAGE TO THE LIMIT IN NONLINEAR VARIATIONAL PROBLEMS
• Existence and multiplicity of solutions for a Neumann problem involving the \(p(x)\)-Laplace operator
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
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