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BOUNDS on the CRITICAL TIMES for the GENERAL FISHER-KPP EQUATION

Journal Article


Abstract


  • The Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) equation is one of the prototypical reaction-diffusion equations and is encountered in many areas, primarily in population dynamics. An important consideration for the phenomena modelled by diffusion equations is the length of the diffusive process. In this paper, three definitions of the critical time are given, and bounds are obtained by a careful construction of the upper and lower solutions. The comparison functions satisfy the nonlinear, but linearizable, partial differential equations of Fisher-KPP type. Results of the numerical simulations are displayed. Extensions to some classes of reaction-diffusion systems and an application to a spatially heterogeneous harvesting model are also presented.

Publication Date


  • 2021

Citation


  • Rodrigo, M. R. (2021). BOUNDS on the CRITICAL TIMES for the GENERAL FISHER-KPP EQUATION. ANZIAM Journal, 63(4), 448-468. doi:10.1017/S1446181121000365

Scopus Eid


  • 2-s2.0-85119062810

Web Of Science Accession Number


Start Page


  • 448

End Page


  • 468

Volume


  • 63

Issue


  • 4

Place Of Publication


Abstract


  • The Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) equation is one of the prototypical reaction-diffusion equations and is encountered in many areas, primarily in population dynamics. An important consideration for the phenomena modelled by diffusion equations is the length of the diffusive process. In this paper, three definitions of the critical time are given, and bounds are obtained by a careful construction of the upper and lower solutions. The comparison functions satisfy the nonlinear, but linearizable, partial differential equations of Fisher-KPP type. Results of the numerical simulations are displayed. Extensions to some classes of reaction-diffusion systems and an application to a spatially heterogeneous harvesting model are also presented.

Publication Date


  • 2021

Citation


  • Rodrigo, M. R. (2021). BOUNDS on the CRITICAL TIMES for the GENERAL FISHER-KPP EQUATION. ANZIAM Journal, 63(4), 448-468. doi:10.1017/S1446181121000365

Scopus Eid


  • 2-s2.0-85119062810

Web Of Science Accession Number


Start Page


  • 448

End Page


  • 468

Volume


  • 63

Issue


  • 4

Place Of Publication