TY - JOUR AU - Acerbi, E. AU - Mingione, G. PY - 2002 DA - 2002// TI - Regularity results for stationary electrorheological fluids JO - Arch. Ration. Mech. Anal. VL - 164 UR - https://doi.org/10.1007/s00205-002-0208-7 DO - 10.1007/s00205-002-0208-7 ID - Acerbi2002 ER - TY - JOUR AU - Antontsev, S. AU - Shmarev, S. PY - 2009 DA - 2009// TI - Anisotropic parabolic equations with variable nonlinearity JO - Publ. Mat. VL - 53 UR - https://doi.org/10.5565/PUBLMAT_53209_04 DO - 10.5565/PUBLMAT_53209_04 ID - Antontsev2009 ER - TY - JOUR AU - Antontsev, S. N. AU - Shmarev, S. I. PY - 2005 DA - 2005// TI - A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions JO - Nonlinear Anal. VL - 60 UR - https://doi.org/10.1016/j.na.2004.09.026 DO - 10.1016/j.na.2004.09.026 ID - Antontsev2005 ER - TY - JOUR AU - Antontsev, S. N. AU - Shmarev, S. I. PY - 2011 DA - 2011// TI - Parabolic equations with double variable nonlinearities JO - Math. Comput. Simul. VL - 81 UR - https://doi.org/10.1016/j.matcom.2010.12.015 DO - 10.1016/j.matcom.2010.12.015 ID - Antontsev2011 ER - TY - JOUR AU - Antontsev, S. N. AU - Zhikov, V. V. PY - 2005 DA - 2005// TI - Higher integrability for parabolic equations of p(x,t)$p(x,t)$-Laplacian type JO - Adv. Differ. Equ. VL - 10 ID - Antontsev2005 ER - TY - JOUR AU - Aramaki, J. PY - 2015 DA - 2015// TI - Hölder continuity with exponent (1+α)/2$(1+\alpha )/2$ in the time variable for solutions of parabolic equations JO - Electron. J. Differ. Equ. VL - 2015 UR - https://doi.org/10.1186/s13662-015-0393-y DO - 10.1186/s13662-015-0393-y ID - Aramaki2015 ER - TY - JOUR AU - Bendahmane, M. AU - Wittbold, P. AU - Zimmermann, A. PY - 2010 DA - 2010// TI - Renormalized solutions for a nonlinear parabolic equation with variable exponents and L1$L^{1}$-data JO - J. Differ. Equ. VL - 249 UR - https://doi.org/10.1016/j.jde.2010.05.011 DO - 10.1016/j.jde.2010.05.011 ID - Bendahmane2010 ER - TY - JOUR AU - Chen, Y. AU - Levine, S. AU - Rao, M. PY - 2006 DA - 2006// TI - Variable exponent, linear growth functionals in image restoration JO - SIAM J. Appl. Math. VL - 66 UR - https://doi.org/10.1137/050624522 DO - 10.1137/050624522 ID - Chen2006 ER - TY - JOUR AU - Droniou, J. AU - Eymard, R. AU - Talbot, K. S. PY - 2016 DA - 2016// TI - Convergence in C([0,T];L2(Ω))$C([0, T];L^{2}(\Omega ))$ of weak solutions to perturbed doubly degenerate parabolic equations JO - J. Differ. Equ. VL - 260 UR - https://doi.org/10.1016/j.jde.2016.02.004 DO - 10.1016/j.jde.2016.02.004 ID - Droniou2016 ER - TY - JOUR AU - Fan, X. L. AU - Zhao, D. PY - 2001 DA - 2001// TI - On the spaces Lp(x)(Ω)${L^{p(x)}(\Omega )}$ and Wm,p(x)${W^{m,p(x)}}$ JO - J. Math. Anal. Appl. VL - 263 UR - https://doi.org/10.1006/jmaa.2000.7617 DO - 10.1006/jmaa.2000.7617 ID - Fan2001 ER - TY - JOUR AU - Gianni, R. AU - Tedeev, A. F. AU - Vespri, V. PY - 2016 DA - 2016// TI - Asymptotic expansion of solutions to the Cauchy problem for doubly degenerate parabolic equations with measurable coefficients JO - Nonlinear Anal. VL - 138 UR - https://doi.org/10.1016/j.na.2015.09.006 DO - 10.1016/j.na.2015.09.006 ID - Gianni2016 ER - TY - JOUR AU - Harjulehto, T. AU - Hästö, P. AU - Koskenoja, M. AU - Varonen, S. PY - 2006 DA - 2006// TI - The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values JO - Potential Anal. VL - 25 UR - https://doi.org/10.1007/s11118-006-9023-3 DO - 10.1007/s11118-006-9023-3 ID - Harjulehto2006 ER - TY - JOUR AU - Kovácik, O. AU - Rákosník, J. PY - 1991 DA - 1991// TI - On spaces Lp(x)${L^{p(x)}}$ and Wk,p(x)${W^{k,p(x)}}$ JO - Czechoslov. Math. J. VL - 41 UR - https://doi.org/10.21136/CMJ.1991.102493 DO - 10.21136/CMJ.1991.102493 ID - Kovácik1991 ER - TY - JOUR AU - Le, C. N. AU - Quach, V. C. AU - Le, X. T. PY - 2020 DA - 2020// TI - Potential well method for p(x)$p(x)$-Laplacian equations with variable exponent sources JO - Nonlinear Anal., Real World Appl. VL - 56 UR - https://doi.org/10.1016/j.nonrwa.2020.103155 DO - 10.1016/j.nonrwa.2020.103155 ID - Le2020 ER - TY - JOUR AU - Li, Q. PY - 2018 DA - 2018// TI - Weak Harnack estimates for supersolutions to doubly degenerate parabolic equations JO - Nonlinear Anal. VL - 170 UR - https://doi.org/10.1016/j.na.2017.12.017 DO - 10.1016/j.na.2017.12.017 ID - Li2018 ER - TY - JOUR AU - Lian, S. AU - Gao, W. AU - Yuan, H. AU - Cao, C. PY - 2012 DA - 2012// TI - Existence of solutions to an initial Dirichlet problem of evolutional p(x)$p(x)$-Laplace equations JO - Ann. Inst. Henri Poincaré, Anal. Non Linéaire VL - 29 UR - https://doi.org/10.1016/j.anihpc.2012.01.001 DO - 10.1016/j.anihpc.2012.01.001 ID - Lian2012 ER - TY - JOUR AU - Liu, B. AU - Dong, M. PY - 2019 DA - 2019// TI - A nonlinear diffusion problem with convection and anisotropic nonstandard growth conditions JO - Nonlinear Anal., Real World Appl. VL - 48 UR - https://doi.org/10.1016/j.nonrwa.2019.01.020 DO - 10.1016/j.nonrwa.2019.01.020 ID - Liu2019 ER - TY - JOUR AU - Otto, F. PY - 1996 DA - 1996// TI - L1$L^{1}$-Contraction and uniqueness for quasilinear elliptic–parabolic equations JO - J. Differ. Equ. VL - 131 UR - https://doi.org/10.1006/jdeq.1996.0155 DO - 10.1006/jdeq.1996.0155 ID - Otto1996 ER - TY - BOOK AU - Ruzicka, M. PY - 2000 DA - 2000// TI - Electrorheological Fluids: Modeling and Mathematical Theory PB - Springer CY - Berlin UR - https://doi.org/10.1007/BFb0104029 DO - 10.1007/BFb0104029 ID - Ruzicka2000 ER - TY - JOUR AU - Shang, H. AU - Cheng, J. PY - 2015 DA - 2015// TI - Cauchy problem for doubly degenerate parabolic equation with gradient source JO - Nonlinear Anal. VL - 113 UR - https://doi.org/10.1016/j.na.2014.10.006 DO - 10.1016/j.na.2014.10.006 ID - Shang2015 ER - TY - JOUR AU - Tersenov, A. S. PY - 2016 DA - 2016// TI - The one dimensional parabolic p(x)$p(x)$-Laplace equation JO - Nonlinear Differ. Equ. Appl. VL - 23 UR - https://doi.org/10.1007/s00030-016-0377-y DO - 10.1007/s00030-016-0377-y ID - Tersenov2016 ER - TY - JOUR AU - Tersenov, A. S. AU - Tersenov, A. S. PY - 2017 DA - 2017// TI - Existence of Lipschitz continuous solutions to the Cauchy–Dirichlet problem for anisotropic parabolic equations JO - J. Funct. Anal. VL - 272 UR - https://doi.org/10.1016/j.jfa.2017.02.014 DO - 10.1016/j.jfa.2017.02.014 ID - Tersenov2017 ER - TY - JOUR AU - Zhan, H. PY - 2017 DA - 2017// TI - The stability of the anisotropic parabolic equation with the variable exponent JO - Bound. Value Probl. VL - 2017 UR - https://doi.org/10.1186/s13661-017-0868-8 DO - 10.1186/s13661-017-0868-8 ID - Zhan2017 ER - TY - JOUR AU - Zhan, H. PY - 2017 DA - 2017// TI - Solutions to polytropic filtration equations with a convection term JO - Electron. J. Differ. Equ. VL - 2017 UR - https://doi.org/10.1186/s13662-017-1273-4 DO - 10.1186/s13662-017-1273-4 ID - Zhan2017 ER - TY - JOUR AU - Zhan, H. PY - 2018 DA - 2018// TI - Infiltration equation with degeneracy on the boundary JO - Acta Appl. Math. VL - 153 UR - https://doi.org/10.1007/s10440-017-0124-3 DO - 10.1007/s10440-017-0124-3 ID - Zhan2018 ER - TY - JOUR AU - Zhan, H. PY - 2019 DA - 2019// TI - The stability of the solutions of an anisotropic diffusion equation JO - Lett. Math. Phys. VL - 109 UR - https://doi.org/10.1007/s11005-018-1135-3 DO - 10.1007/s11005-018-1135-3 ID - Zhan2019 ER - TY - JOUR AU - Zhan, H. AU - Feng, Z. PY - 2017 DA - 2017// TI - Solutions of evolutionary p(x)$p(x)$-Laplacian equation based on the weighted variable exponent space JO - Z. Angew. Math. Phys. VL - 68 UR - https://doi.org/10.1007/s00033-017-0885-6 DO - 10.1007/s00033-017-0885-6 ID - Zhan2017 ER - TY - JOUR AU - Zhan, H. AU - Feng, Z. PY - 2019 DA - 2019// TI - The stability of the solutions of convection–diffusion equation JO - Nonlinear Anal. VL - 182 UR - https://doi.org/10.1016/j.na.2018.12.008 DO - 10.1016/j.na.2018.12.008 ID - Zhan2019 ER - TY - JOUR AU - Zhan, H. AU - Feng, Z. PY - 2020 DA - 2020// TI - The well-posedness problem of an anisotropic parabolic equation JO - J. Differ. Equ. VL - 268 UR - https://doi.org/10.1016/j.jde.2019.08.014 DO - 10.1016/j.jde.2019.08.014 ID - Zhan2020 ER - TY - JOUR AU - Zhan, H. AU - Feng, Z. PY - 2020 DA - 2020// TI - Stability of anisotropic parabolic equations without boundary conditions JO - Electron. J. Differ. Equ. VL - 2020 ID - Zhan2020 ER - TY - JOUR AU - Zhan, H. AU - Ouyang, M. PY - 2018 DA - 2018// TI - The stability of the solutions for a porous medium equation with a convection term JO - Discrete Dyn. Nat. Soc. VL - 2018 ID - Zhan2018 ER - TY - JOUR AU - Zhan, H. AU - Wen, J. PY - 2016 DA - 2016// TI - Evolutionary p(x)$p(x)$-Laplacian equation free from the limitation of the boundary value JO - Electron. J. Differ. Equ. VL - 2016 UR - https://doi.org/10.1186/s13662-016-0862-y DO - 10.1186/s13662-016-0862-y ID - Zhan2016 ER - TY - JOUR AU - Zhang, C. AU - Zhuo, S. AU - Xue, X. PY - 2014 DA - 2014// TI - Global gradient estimates for the parabolic p(x,t)$p(x,t)$-Laplacian equation JO - Nonlinear Anal. VL - 105 UR - https://doi.org/10.1016/j.na.2014.04.005 DO - 10.1016/j.na.2014.04.005 ID - Zhang2014 ER - TY - JOUR AU - Zhikov, V. V. PY - 2004 DA - 2004// TI - On the density of smooth functions in Sobolev–Orlicz spaces JO - Zap. Nauč. Semin. POMI VL - 310 ID - Zhikov2004 ER - TY - JOUR AU - Zhou, Z. AU - Guo, Z. AU - Wu, B. PY - 2018 DA - 2018// TI - A doubly degenerate diffusion equation in multiplicative noise removal models JO - J. Math. Anal. Appl. VL - 458 UR - https://doi.org/10.1016/j.jmaa.2017.08.049 DO - 10.1016/j.jmaa.2017.08.049 ID - Zhou2018 ER - TY - JOUR AU - Zou, W. AU - Li, L. PY - 2017 DA - 2017// TI - Existence and uniqueness of solutions for a class of doubly degenerate parabolic equations JO - J. Math. Anal. Appl. VL - 446 UR - https://doi.org/10.1016/j.jmaa.2016.10.002 DO - 10.1016/j.jmaa.2016.10.002 ID - Zou2017 ER -