On the shape of the least-energy solutions tosome singularly perturbed mixed problems
Luigi Montoro · Communications on Pure & Applied Analysis · 2010
In this paper we want to \emph{characterize} and\emph{visualize} the shape of some solutions to a singularlyperturbed problem \eqref{eq:pe} with mixed Dirichlet and Neumannboundary conditions. Such type of problem arisesin several situations as reaction-diffusion systems, nonlinear heat conduction and also as limit of reaction-diffusion systems coming from chemotaxis.In particular we are interested in showing the location andthe shape of {\it least energy solutions} when the singularperturbation parameter goes to zero, analyzing the geometricaleffect of the \emph{curved boundary} of the domain.