Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources

• Main Authors: Ida de Bonis, Adrian Muntean
• Format: Article
• Language: English
• Published: Texas State University 2017-09-01
• Series: Electronic Journal of Differential Equations
• Subjects: Reaction-diffusion systems; singular parabolic equations; weak solutions
• Online Access: http://ejde.math.txstate.edu/Volumes/2017/202/abstr.html

We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i) the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii) the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.