Blow-up of solutions to semi-discrete parabolic-elliptic Keller-Segel models | Zendy

Ansgar Jüngel | Zendy; Oliver Leingang | Zendy

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Blow-up of solutions to semi-discrete parabolic-elliptic Keller-Segel models

Author(s) -

Ansgar Jüngel,

Oliver Leingang

Publication year - 2019

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2019029

Subject(s) - mathematics , space (punctuation) , euler's formula , backward euler method , space time , spacetime , mathematical analysis , finite element method , order (exchange) , euler equations , physics , computer science , thermodynamics , finance , quantum mechanics , chemical engineering , engineering , economics , operating system

The existence of weak solutions and upper bounds for the blow-up time for time-discrete parabolic-elliptic Keller-Segel models for chemotaxis in the two-dimensional whole space are proved. For various time discretizations, including the implicit Euler, BDF, and Runge-Kutta methods, the same bounds for the blow-up time as in the continuous case are derived by discrete versions of the virial argument. The theoretical results are illustrated by numerical simulations using an upwind finite-element method combined with second-order time discretizations.

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