References
- Lions JL. Queleues méthodes de résolution des problèmes aux limites nonlineaires. Paris: Dunod; 1969.
- Kinderlehrer D, Stampacchia G. An introduction to variational inequalities. New York (NY): Academic Press; 1980.
- Friedman A. Variational principles and free boundary value problems. New York (NY): Wiley Interscience; 1983.
- Rudd M, Schimtt K. Variational inequalities of elliptic and parabolic type. Taiwanese Journal of Mathematics. 2002;6(3):287–322.
- Shahgholian H. Analysis of the free boundary fpr the p-parabolic variational problem (p ≥ 2).. Revista Matematica Iberoamericana. 2003;19:797–812.
- Korte R, Kuusi T, Siljiander J. Obstacle problem for nonlinear parabolic equations. Journal of Differential Equations. 2009;246:3668–3680.
- Zhikov V. Averaging of functionals of the calculus of variations and elasticity theory. Mathematics of the USSR-Izvestiya. 1987;29:675–710.
- Zhikov V. On Lavrentiev’s phenomenon. Russian Journal of Mathematical Physics. 1995;3:249–269.
- Rajagopal K. Rüz̆ika M. On the modeling of electrorheological materials. Mechanics Research. Communications. 1996;23(4):401–407.
- Zhikov V. Solvability of the three-dimensional thermistor problem. Proceedings of the Steklov Institute of Mathematics. 2008;261(1):101–114.
- Chen YM, Levine S, Rao M. Variable exponent linear growth functionals in inmage restoration. SIMA Journal of Applied Mathematics. 2006;66:1383–1406.
- Fu YQ, Pan N. Existence of solutions for nonlinear parabolic problems with p(x)-growth. Journal of Mathematical Analysis and Applications. 2010;362:313–326.
- Fu YQ, Pan N. Local boundedness of weak solutions for nonlinear parabolic problem with p(x)-growth. Journal of Inequalities and Applications. 2010;57:16. Article ID 163296.
- Diening L, Harjulehto P, Hästö P, Rüz̆ic̆ka M. Lebesgue and Sobolev spaces with variable exponents. Lecture Notes in Mathematics. Vol. 2017. Berlin: Springer; 2011.
- Fu YQ, Xiang MQ, Pan N. Regularity of weak solutions for nonlinear parabolic problem with p(x)-growth. EJQTDE. 2012;4:1–26.
- Diening L, Nägele P, Rüz̆ic̆ka M. Monotone operator theory for unsteady problems in variable exponent spaces. CVEE. 2011;57:1–23.
- Antontsev S, Shmarev S. Parabolic equations with anisotropic nonstandard growth conditions. Free Boundary Problems. 2007;60:33–44.
- Antontsev S, Shmarev S. Anistropic parabolic equations with variable nonlinearity. Publicacions Matemàtiques. 2009;53:355–399.
- Buhrii OM, Lavrenyuk SP. On a parabolic variational inequality that generalizes the equation of polytropic filtration. Ukrainian Mathematical Journal. 2001;53(7):1027–1042.
- Buhrii OM, Mashiyev RA. Uniqueness of solutions of parabolic variational inequality with variable exponent of nonlinearity. Nonlinear Analysis. 2009;70:2325–2331.
- Mashiyev RA, Buhrii OM. Existence of solutions of the parabolic variational inequality with variable exponent of nonlinearity. Journal of Mathematical Analysis and Applications. 2011;377:450–463.
- Kováčik O, Rákosnik J. On spaces Lp(x) and Wk,p(x). Czechoslovak Mathematical Journal. 1991;41(116):592–618.
- Fan XL, Zhao D. On the spaces Lp(x)(Ω) and Wm,p(x)(Ω).. Journal of Mathematical Analysis and Applications. 2001;263:424–446.
- Landes R. On the existence of weak solutions for quasilinear parabolic boundary problems. Proceedings of the Royal Society of Edinburgh Section A. 1981;89:217–237.