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Start Over Author "Corrias L" Topic 92c17
3 results on '"Corrias L"'

2. L p and L ∞ a priori estimates for some chemotaxis models and applications to the Cauchy problem

Author

Corrias, L, Perthame, Benoît, Zaag, Hatem, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), and Zaag, Hatem

Subjects
angiogenesis, Chemotaxis, 92C50, degenerate parabolic equations, 35Q80, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], global weak solutions, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], blow-up AMS subject classifications 35B60, 92C17
Abstract

International audience; In this note, we generalize some a priori estimates from our earlier work concerning two models of chemotaxis. We also give a new L ∞ bound for these models which yields uniqueness for one of them.

Published
2004

3. Existence, uniqueness and asymptotic behavior of the solutions to the fully parabolic Keller–Segel system in the plane.

Author

Corrias, L., Escobedo, M., and Matos, J.

Subjects
*EXISTENCE theorems, *UNIQUENESS (Mathematics), *PARABOLIC differential equations, *KERNEL (Mathematics), *MATHEMATICAL proofs
Abstract

In the present article we consider several issues concerning the doubly parabolic Keller–Segel system (1.1)–(1.2) in the plane, when the initial data belong to critical scaling-invariant Lebesgue spaces. More specifically, we analyze the global existence of integral solutions, their optimal time decay, uniqueness and positivity, together with the uniqueness of self-similar solutions. In particular, we prove that there exist integral solutions of any mass, provided that ε > 0 is sufficiently large. With those results at hand, we are then able to study the large time behavior of global solutions and prove that in the absence of the degradation term ( α = 0 ) the solutions behave like self-similar solutions, while in the presence of the degradation term ( α > 0 ) the global solutions behave like the heat kernel. [ABSTRACT FROM AUTHOR]

Published
2014
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