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Pattern forming instabilities driven by non-diffusive interactions

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  • In analogy to the analysis of minimal conditions for the formation of diffusion driven instabilities in the sense of Turing, in this paper minimal conditions for a class of kinetic equations with mass conservation are discussed, whose solutions show patterns with a characteristic wavelength. The related linearized systems are analyzed, and the minimal number of equations is derived, which is needed for specific patterns to occur.
    Mathematics Subject Classification: Primary: 35L45, 35P20, 35B20, 35B36; Secondary: 92C15, 92C17.


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