Displaying similar documents to “Harmonic spaces associated with parabolic and elliptic differential operators.”

Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system

Yutaro Chiyo (2023)

Archivum Mathematicum

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This paper deals with a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system. Boundedness, stabilization and blow-up in this system of the fully parabolic and parabolic-elliptic-elliptic versions have already been proved. The purpose of this paper is to derive boundedness and stabilization in the parabolic-parabolic-elliptic version.

A note on the density of the parabolic area integral.

Ileana Iribarren (2001)

Collectanea Mathematica

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The density of the area integral for parabolic functions is defined in analogy with the case of harmonic functions. We prove its equivalence with the local time of the associated martingale. Using probabilistic methods, we show its equivalence in L p -norm with the parabolic area function for p>1.

On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis

Piotr Biler, Lorenzo Brandolese (2009)

Studia Mathematica

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We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller-Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.