Strongly quasilinear parabolic systems

Author:

Balaadich Farah, ,Azroul Elhoussine, ,

Abstract

"Using the theory of Young measures, we prove the existence of solutions to a strongly quasilinear parabolic system \[\frac{\partial u}{\partial t}+A(u)=f,\] where $A(u)=-\text{div}\,\sigma(x,t,u,Du)+\sigma_0(x,t,u,Du)$, $\sigma(x,t,u,Du)$ and $\sigma_0(x,t,u,Du)$ are satisfy some conditions and $f\in L^{p'}(0,T;W^{-1,p'}(\Omega;\R^m))$."

Publisher

Babes-Bolyai University

Subject

General Mathematics

Reference27 articles.

1. "[1] Adams, R.A., Fournier, J.J.F., Fournier, Sobolev spaces, 2nd ed., Vol. 140, Pure and Applied Mathematics, Amsterdam, Elsevier, Academic Press, 2003.

2. [2] Aharouch, L., Azroul, E., Rhoudaf, M., Existence result for variational degenerated parabolic problems via pseudo-monotonicity, EJDE, 14(2006), 9-20, ISSN: 1072-6691.

3. [3] Amann, H., Ordinary Differential Equations: An Introduction to Nonlinear Analysis, Berlin, De Gruyter, 1990.

4. [4] Azroul, E., Balaadich, F., Weak solutions for generalized p-Laplacian systems via Young measures, Moroccan J. of Pure and Appl. Anal., 4(2018), no. 2, 76-83.

5. [5] Azroul, E., Balaadich, F., Strongly quasilinear parabolic systems in divergence form with weak monotonicity, Khayyam J. Math., 6(2020), no 1, 57-72.

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