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 in nite 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.
Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources / De Bonis, I.; Muntean, A.. - In: ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 1072-6691. - 2017:(2017).
Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources
De Bonis I.;
2017
Abstract
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 in nite 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.