Title: Convergence towards heterogeneous patterns for a degenerate reaction-diffusion system

Abstract: In this talk, I will present recent results on the dynamics of a degenerate reaction-diffusion system with hysteresis, modeling the biological evolution of a forest ecosystem. Using a generalized Mountain Pass Theorem, valid for elliptic equations admitting a discontinuous right-hand side, and generalized Clarke gradients, I prove the existence of an infinite and continuous family of heterogeneous steady states, and I establish the weak convergence of particular global solutions towards those heterogeneous states. The nonlinear dynamics of this model are numerically illustrated and interpreted in terms of forest ecology, with a focus on the morphogenesis of the ecotone, corresponding to the ecological boundary between the forest ecosystem and its neighbor ecosystem. This work is supported by the French National Agency (TOUNDRA project, ANR-24-CE56-3042).