Diffusion-Driven Blow-Up for a Nonlocal Fisher-KPP Type Model
Nikos I. Kavallaris, Evangelos Latos, Takashi Suzuki
Abstract
The purpose of the current paper is to unveil the key mechanism which is responsible for the occurrence of Turing-type instability for a nonlocal Fisher-KPP model. In particular, we prove that the solution of the considered nonlocal Fisher-KPP equation in the neighborhood of a constant stationary solution is destabilized via a diffusion-driven blow-up. It is also shown that the observed diffusion-driven blow-up is complete, while its blow-up rate is completely classified. Finally, the detected diffusion-driven instability results in the formation of unstable blow-up patterns, which are also identified through the determination of the blow-up profile of the solution.
Topics & Concepts
MathematicsInstabilityDiffusionType (biology)Constant (computer programming)Mathematical analysisPhysicsMechanicsThermodynamicsComputer scienceBiologyProgramming languageEcologyMathematical and Theoretical Epidemiology and Ecology ModelsStability and Controllability of Differential EquationsMathematical Biology Tumor Growth