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On linearizing systems of diffusion equations. (English) Zbl 1092.35501

Summary: We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we use the equivalence transformations of the second generation potential system to derive forms of this system that can be linearized. In turn, these transformations lead to nonlocal mappings that linearize the original system.

MSC:

35A30 Geometric theory, characteristics, transformations in context of PDEs
35K57 Reaction-diffusion equations
92B05 General biology and biomathematics
35A22 Transform methods (e.g., integral transforms) applied to PDEs
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