Existence, uniqueness and positivity on a free-boundary high order diffusion cooperative system

Results in Applied Mathematics

Antonio Naranjo Redondo¹  José Luis Díaz Palencia² 

[1] Escuela Politécnica Superior, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1,800, 28223, Pozuelo de Alarcón, Madrid, Spain;Corresponding author.;

关键词: Bi-laplacian;    Instabilities;    Positivity;    Kernel;    Uniqueness;   

DOI  :  

来源: DOAJ

【 摘 要 】

We study existence, uniqueness and positivity conditions for a cooperative system formulated with a high order diffusion. In addition, we show and characterize the instabilities due to the high order diffusion for which a positivity and a comparison principle hold after rescaling. Instabilities shall be understood as the oscillatory behaviour of solutions acting as an inherent feature driven by complex exponential bundles of solutions. Firstly, a shooting method approach is used to show the existence of such instabilities. Afterwards, the existence of solutions is assessed in the self-similar approach and characterized by analytical and numerical evidences for a single equation in and for the complete system. Finally, a positive kernel is shown to exist and a sharp estimation is obtained.

【 授权许可】

Unknown