The Fisher-KPP problem with doubly nonlinear diffusion
By A. Audrito, Juan Luis V'azquez. 2016
61 citations recorded by the source corpus.
Abstract The famous Fisher-KPP reaction–diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it possesses a family of travelling waves that describe the asymptotic behaviour of a large class solutions 0 ≤ u ( x , t ) ≤ 1 of the problem posed in the real line. The existence of propagation waves with finite speed has been confirmed in some related models and disproved in others. We investigate here the corresponding theory when the linear diffusion is replaced by the “slow” doubly nonlinear diffusion and we find travelling waves that represent the wave propagation of more general solutions even when we extend the study to several space dimensions. A similar study is performed in the critical case that we call “pseudo-linear”, i.e., when the operator is still nonlinear but has homogeneity one. With respect to the classical model and the “pseudo-linear” case, the “slow” travelling waves exhibit free boundaries.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a3b4004284cd4a1b8ca5f1210088c39fcf358288
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In Applied Mathematics
- A. Audrito
- Juan Luis V'azquez
- Matteo Bonforte
- G. Grillo
- Luis Caffarelli
- Razvan Gabriel Iagar
- Alessio Figalli
- Jean Dolbeault
In Mathematical Physics
Citations in the corpus
- The Fisher–KPP problem with doubly nonlinear “fast” diffusion (2016, background): “The existence of propagation wave with finite speed has been confirmed in the cases of “slow” and “pseudo-linear” doubly nonlinear diffusion too, see [7].”
- Infinite Speed of Propagation and Regularity of Solutions to the Fractional Porous Medium Equation in General Domains (2015, unknown): “The question of finite versus infinite speed of propagation on R has also been investigated in [19, 20, 60, 62] for a different model of fractional PME introduced by Caffarelli and Vazquez [19,20]; an equivalence among self-similar solutions between the two main models of nonlocal porous medium equa”