Stationary states of reaction-diffusion and Schr\"odinger systems with inhomogeneous or controlled diffusion

Alexandre Montaru; Boyan Sirakov

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arXiv · 1504.05791

Stationary states of reaction-diffusion and Schr\"odinger systems with inhomogeneous or controlled diffusion

Alexandre Montaru·Boyan Sirakov

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Abstract

We obtain classification, solvability and nonexistence theorems for positive stationary states of reaction-diffusion and Schr\"odinger 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.

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Alexandre Montaru, Boyan Sirakov. 2015-04-22. Stationary states of reaction-diffusion and Schr\"odinger systems with inhomogeneous or controlled diffusion. https://arxiv.org/abs/1504.05791

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