Solvability of a coupled quasilinear reaction–diffusion system

Abstract

The aim of this paper is to investigate the existence, uniqueness, and long-time behaviour of the classical solutions to a coupled system of four quasilinear parabolic equations. Two of them are solved in a domain and the other two are determined on the domain boundary. Such coupled systems arise in modelling of surface reactions between two reactants.

Keywords:

• Coupled parabolic systems
• positive solutions
• reaction–diffusion system

AMS CLASSIFICATIONS:

• 35K20
• 35B09

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Research Council of Lithuania (project No. S-MIP-17-65).