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On a class of nonlocal diffusion equations
José Francisco Rodrigues
CMAF/University of Lisbon
Nonlocal reaction-diffusion problems arise in the modeling of natural
phenomena. We consider the existence and the approximation, via
appropriate reaction-diffusion systems, of solutions to a class of
parabolic equations with nonlocal nonlinearities, which in the Lipschitz
continuous case are unique. We also give a counter-example to the
uniqueness in the case of nonlocal discontinuous reaction term and we give
examples of application in mathematical models of combustion theory and of
morphogenesis in excitable media.