Abstract
In this communication, we consider the stationary problem of a non-linear parabolic system which arises in the context of dry-land vegetation. In the first part, we examine the existence and multiplicity of biomass stationary solutions, in terms of the precipitation rate parameter \(p\), for a localized simplification of the system, with non-homogeneous rate of biomass loss. In fact, we show that under appropriate conditions on fixed parameters of the problem, multiple positive solutions exist for a range of the parameter \(p\). In the second part, we consider the case of an idealized “oasis”, \(\omega \subset \subset \varOmega \), where we study the transition of the surface-water height in a neighborhood of the set \(\omega \).
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Acknowledgments
The research of the authors has received funding from the ITN FIRST of the Seventh Framework Programme of the European Community (Grant agreement number 238702). The research of JID was partially supported by the Research Group MOMAT (Ref. 910480), UCM and the project MTM2011-26119 (DGISPI, Spain).
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Diaz, J.I., Kyriazopoulos, P. On an elliptic system related to desertification studies. RACSAM 108, 397–404 (2014). https://doi.org/10.1007/s13398-012-0108-0
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DOI: https://doi.org/10.1007/s13398-012-0108-0