Electron. J. Differential Equations, Vol. 2017 (2017), No. 202, pp. 1-16.

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

Ida de Bonis, Adrian Muntean

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.

Submitted March 20 2017. Published September 6, 2017.
Math Subject Classifications: 35K57, 35K67, 35D30.
Key Words: Reaction-diffusion systems; singular parabolic equations; weak solutions.

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Ida de Bonis
Universitá Giustino Fortunato
email: i.debonis@unifortunato.eu
Adrian Muntean
Karlstad University
email: adrian.muntean@kau.se

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