Transition fronts in inhomogeneous Fisher-KPP reaction-diffusion equations. (English) Zbl 1252.35110
Summary: We use a new method in the study of Fisher-KPP reaction-diffusion equations to prove existence of transition fronts for inhomogeneous KPP-type non-linearities in one spatial dimension. We also obtain new estimates on entire solutions of some KPP reaction-diffusion equations in several spatial dimensions. Our method is based on the construction of sub- and super-solutions to the non-linear PDE from solutions of its linearization at zero.
MSC:
| 35C07 | Traveling wave solutions |
| 35K57 | Reaction-diffusion equations |
| 35B08 | Entire solutions to PDEs |
| 35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
Keywords:
Kolmogorov-Petrovskii-Piskunov; one spatial dimension; several spatial dimensions; sub- and super-solutionsReferences:
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