Stationary states of reaction-diffusion and Schrödinger systems with inhomogeneous or controlled diffusion

Boyan Sirakov (1) , Alexandre Montaru (2)

1 Departamento de Matematica
2 LAGA - Laboratoire Analyse, Géométrie et Applications

We obtain classification, solvability and nonexistence theorems for positive stationary states of reaction-diffusion and Schrödinger systems involving a balance between repulsive and attractive terms. This class of systems contains PDE arising in biological models of Lotka-Volterra type, in physical models of Bose-Einstein condensates and in models of chemical reactions. We show, with different proofs, that the results obtained in [ARMA, 213 (2014), 129-169] for models with homogeneous diffusion are valid for general heterogeneous media, and even for controlled inhomogeneous diffusions.

Domaines: Equations aux dérivées partielles [math.AP]

Boyan Sirakov, Alexandre Montaru. Stationary states of reaction-diffusion and Schrödinger systems with inhomogeneous or controlled diffusion. 2015. ⟨hal-01219630⟩