Stability of non-Newtonian fluid and electrorheological fluid mixed-type equation

References

• Ruzicka M. Electrorheological fluids: modeling and mathematical theory. Berlin: Springer; 2000. (Lecture Notes in Mathematics; vol. 1748).
   Google Scholar
• Wu Z, Zhao J, Yin J, et al. Nonlinear diffusion equations. Singapore: Word Scientific Publishing; 2001.
   Google Scholar
• Acerbi E, Mingione G. Regularity results for stationary electrorheological fluids. Arch Ration Mech Anal. 2002;164:213–259.
   Web of Science ®Google Scholar
• Alghamdi AM, Gala S, Kim J-M, et al. The anisotropic integrability logarithmic regularity criterion to the 3D micropolar fluid equations. AIMS Math. 2020;5(1):359–375.
   Web of Science ®Google Scholar
• Alkis ST, Aris ST. Existence of Lipschitz continuous solutions to the Cauchy–Dirichlet problem for anisotropic parabolic equations. J Funct Anal. 2017;272:3965–3986.
   Web of Science ®Google Scholar
• Antontsev S, Shmarev S. Anisotropic parabolic equations with variable nonlinearity. Publ Mat. 2009;53:355–399.
   Web of Science ®Google Scholar
• Boudjeriou T. Global existence and blow-up of solutions for a parabolic equation involving the fractional p(x)-Laplacian. Appl Anal. 2020. doi:10.1080/00036811.2020.1829601.
   Web of Science ®Google Scholar
• Guo B, Gao W. Extinction and asymptotic behavior of solutions for nonlinear parabolic equations with variable exponent of nonlinearity. Acta Math Sci. 2012;32B:1053–1062.
   Google Scholar
• Ho K, Sim I. On degenerate p(x)-Laplacian equations involving critical growth with two parameters. Nonlinear Anal. 2016;132:95–114.
   Web of Science ®Google Scholar
• Lian S, Gao W, Yuan H, et al. Existence of solutions to an initial Dirichlet problem of evolutional p(x)-Laplace equations. Ann Inst H Poincare Anal Non Lineaire. 2012;29:377–399.
   Web of Science ®Google Scholar
• Ragusa MA, Tachikawa A. Regularity for minimizers for functionals of double phase with variable exponents. Adv Nonlinear Anal. 2020;9:710–728.
   Web of Science ®Google Scholar
• Benedikt J, Bobkov VE, Girg P, et al. Nonuniqueness of solutions of initial-value problems for parabolic p-Laplacian. Electron J Differ Equ. 2015;38:1–7.
   Google Scholar
• Yin J, Wang C. Evolutionary weighted p-Laplacian with boundary degeneracy. J Differ Equ. 2007;237:421–445.
   Web of Science ®Google Scholar
• Zhan H. The uniqueness of the solution to the diffusion equation with a damping term. Appl Anal. 2019;98:1333–1246.
   Web of Science ®Google Scholar
• Zhan H, Feng Z. Degenerate non-Newtonian fluid equation on the half space. Dyn Partial Differ Equ. 2018;15:215–233.
   Web of Science ®Google Scholar
• Zhan H. Infiltration equation with degeneracy on the boundary. Acta Appl Math. 2018;153:147–161.
   Web of Science ®Google Scholar
• Zhan H. Solutions to polytropic filtration equations with a convection term. Electron J Differ Equ. 2017;207:1–10.
   Google Scholar
• Andreianov B, Bendahmane M, Karlsen KH, et al. Well-posedness results for triply nonlinear degenerate parabolic equations. J Differ Equ. 2009;247:277–302.
   Web of Science ®Google Scholar
• Antonelli F, Barucci E, Mancino ME. A comparison result for FBSDE with applications to decisions theory. Math Methods Oper Res. 2001;54:407–423.
   Web of Science ®Google Scholar
• Bardos C, Leroux AY, Nedelec JC. First order quasilinear equations with boundary conditions. Commun Partial Differ Equ. 1979;4:1017–1034.
   Google Scholar
• Kobayasi K, Ohwa H. Uniqueness and existence for anisotropic degenerate parabolic equations with boundary conditions on a bounded rectangle. J Differ Equ. 2012;252:137–167.
   Web of Science ®Google Scholar
• Li Y, Wang Q. Homogeneous Dirichlet problems for quasilinear anisotropic degenerate parabolic-hyperbolic equations. J Differ Equ. 2012;252:4719–4741.
   Web of Science ®Google Scholar
• Lions PL, Perthame B, Tadmor E. A kinetic formation of multidimensional conservation laws and related equations. J Am Math Soc. 1994;7:169–191.
   Google Scholar
• Zhao J, Yuan H. The Cauchy problem of some doubly nonlinear degenerate parabolic equations (in Chinese). Chin Anal Math. 1995;16A:179–194.
   Google Scholar
• Wu Z, Zhao J. The first boundary value problem for quasilinear degenerate parabolic equations of second order in several variables. Chin Anal Math. 1983;4B:57–76.
   Google Scholar
• Antontsev S, Shmarev S. Parabolic equations with double variable nonlinearlities. Math Comput Simul. 2011;81:2018–2032.
   Web of Science ®Google Scholar