Electron. J. Differential Equations, Vol. 2018 (2018), No. 113, pp. 1-19.

Existence of weak solutions for quasilinear parabolic systems in divergence form with variable growth

Miaomiao Yang, Yongqiang Fu

Abstract:
In this article we study the existence of weak solutions for quasilinear parabolic system in divergence form with variable growth. By means of Young measures, Galerkin's approximation method and the theory of variable exponents spaces, we obtain the existence of weak solutions.

Submitted November 16, 2017. Published May 10, 2018.
Math Subject Classifications: 35D30, 35K59, 46E35.
Key Words: Variable exponent; Young measures; weak solutions; quasilinear parabolic system; Galerkin's approximation.

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Miaomiao Yang
School of Science
Qilu Institute of Technology
Jinan 250001, China
email: 3d07@163.com
  Yongqiang Fu
Department of Mathematics
Harbin Institute of Technology
Harbin 150001, China
email: fuyongqiang@hit.edu.cn

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