Address: Department of Mathematics, Faculty of Science, University of South Bohemia, Branišovská 1760, 37005 České Budějovice, Czech Republic
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Abstract: We show the location of so called critical points, i.e., couples of diffusion coefficients for which a non-trivial solution of a linear reaction-diffusion system of activator-inhibitor type on an interval with Neumann boundary conditions and with additional non-linear unilateral condition at one or two points on the boundary and/or in the interior exists. Simultaneously, we show the profile of such solutions.
AMSclassification: primary 34B15; secondary 35B36, 92C15.
Keywords: reaction-diffusion system, critical points, unilateral conditions.
DOI: 10.5817/AM2023-2-173