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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Hans W. Alt, Stephan Luckhaus (1983)
Mathematische Zeitschrift
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D. G. Aronson, P. Besala (1967)
Colloquium Mathematicae
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Grzegorz Bartuzel, Andrzej Fryszkowski (1991)
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.
Masashi Misawa (1993)
Mathematische Zeitschrift
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Cvetićanin, Dragan, Obradović, Ratko (1998)
Novi Sad Journal of Mathematics
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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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Uraltseva, N. N.
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P. Besala (1963)
Colloquium Mathematicae
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Sarmila Sahoo (2015)
Curved and Layered Structures
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In this paper free vibration behavior of laminated composite stiffened elliptic parabolic shell has been analyzed in terms of natural frequency and mode shape. Finite element method has been applied using an eight-noded curved quadratic isoparametric element for shell with a three noded curved beam element for stiffener. Cross and angle ply shells with different edge conditions have been studied varying the size and position of the cutouts to arrive at a set of inferences of practical...
Kassmann, Moritz (2007)
Boundary Value Problems [electronic only]
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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).