Ida de Bonis, Adrian Muntean
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 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 Italy email: i.debonis@unifortunato.eu | |
Adrian Muntean Karlstad University Sweden email: adrian.muntean@kau.se |
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