On integro-differential equations of parabolic and elliptic type
H. Ugowski (1970)
Annales Polonici Mathematici
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H. Ugowski (1970)
Annales Polonici Mathematici
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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.
P. Besala, H. Ugowski (1969)
Colloquium Mathematicae
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Hans W. Alt, Stephan Luckhaus (1983)
Mathematische Zeitschrift
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Cvetićanin, Dragan, Obradović, Ratko (1998)
Novi Sad Journal of Mathematics
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Masashi Misawa (1993)
Mathematische Zeitschrift
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Emmanuel Maitre (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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This paper deals with the numerical approximation of mild solutions of elliptic-parabolic equations, relying on the existence results of Bénilan and Wittbold (1996). We introduce a new and simple algorithm based on Halpern's iteration for nonexpansive operators (Bauschke, 1996; Halpern, 1967; Lions, 1977), which is shown to be convergent in the degenerate case, and compare it with existing schemes (Jäger and Kačur, 1995; Kačur, 1999).
Uraltseva, N. N.
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Stanisław Brzychczy (1996)
Annales Polonici Mathematici
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We consider a nonlinear differential-functional parabolic boundary initial value problem (1) ⎧A z + f(x,z(t,x),z(t,·)) - ∂z/∂t = 0 for t > 0, x ∈ G, ⎨z(t,x) = h(x) for t > 0, x ∈ ∂G, ⎩z(0,x) = φ₀(x) for x ∈ G, and the associated elliptic boundary value problem with Dirichlet condition (2) ⎧Az + f(x,z(x),z(·)) = 0 for x ∈ G, ⎨z(x) = h(x) for x ∈ ∂G ⎩ where , G is an open and bounded domain with (0 < α ≤ 1) boundary, the operator Az := ∑j,k=1m ajk(x) (∂²z/(∂xj...
Sapa, Lucjan (2006)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Alexander Zenisek (1987)
Numerische Mathematik
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Arina Arkhipova (2008)
Banach Center Publications
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We consider nondiagonal elliptic and parabolic systems of equations with quadratic nonlinearities in the gradient. We discuss a new description of regular points of solutions of such systems. For a class of strongly nonlinear parabolic systems, we estimate locally the Hölder norm of a solution. Instead of smallness of the oscillation, we assume local smallness of the Campanato seminorm of the solution under consideration. Theorems about quasireverse Hölder inequalities proved by the...
Horn, Werner (2002)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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P. Besala (1975)
Annales Polonici Mathematici
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