EXISTENCE OF WEAK SOLUTIONS TO A NONLINEAR REACTION-DIFFUSION SYSTEM WITH SINGULAR SOURCES

Ida De Bonis, Adrian Muntean
2017 Electronic Journal of Differential Equations   unpublished
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
more » ... e 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.
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