A Construction of Representing Measures for Elliptic and Parabolic Differential Equations.
Peter A. Loeb (1982)
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Peter A. Loeb (1982)
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Peter A. Loeb (1980)
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Kassmann, Moritz (2007)
Boundary Value Problems [electronic only]
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Yutaro Chiyo (2023)
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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.
Hans W. Alt, Stephan Luckhaus (1983)
Mathematische Zeitschrift
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H. Ugowski (1970)
Annales Polonici Mathematici
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Ileana Iribarren (2001)
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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.
Masashi Misawa (1993)
Mathematische Zeitschrift
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P. Besala, H. Ugowski (1969)
Colloquium Mathematicae
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Paolo Acquistapace, Brunello Terreni (1988)
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F.E. BROWDER (1961)
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Hedi Ben Saad, Klaus Janßen (1985)
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Piotr Biler, Lorenzo Brandolese (2009)
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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.
Alessandra Lunardi (1984)
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D.H. SATTINGER (1969)
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