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Z. Abdul-Hadi, D. Bschouty, W. Hengartner (1985)
Matematički Vesnik
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Z. Abdul-Hadi, D. Bschouty, W. Hengartner (1985)
Matematički Vesnik
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Marek Jarnicki, Peter Pflug (1997)
Annales Polonici Mathematici
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We present various characterizations of n-circled domains of holomorphy with respect to some subspaces of .
J. Siciak (1985)
Matematički Vesnik
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A. Zięba (1972)
Colloquium Mathematicae
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M. Prizzi, K. P. Rybakowski (2003)
Studia Mathematica
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We study a family of semilinear reaction-diffusion equations on spatial domains , ε > 0, in lying close to a k-dimensional submanifold ℳ of . As ε → 0⁺, the domains collapse onto (a subset of) ℳ. As proved in [15], the above family has a limit equation, which is an abstract semilinear parabolic equation defined on a certain limit phase space denoted by . The definition of , given in the above paper, is very abstract. One of the objectives of this paper is to give more manageable...
David Gérard-Varet, Nader Masmoudi (2011)
Journal of the European Mathematical Society
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We consider the homogenization of elliptic systems with -periodic coefficients. Classical two-scale approximation yields an error inside the domain. We discuss here the existence of higher order corrections, in the case of general polygonal domains. The corrector depends in a non-trivial way on the boundary. Our analysis substantially extends previous results obtained for polygonal domains with sides of rational slopes.
Kyong T. Hahn, Josephine Mitchell (1973)
Annales Polonici Mathematici
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Eugene Fabes (1972)
Studia Mathematica
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Edgar Lee Stout (2006)
Annales Polonici Mathematici
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We construct a domain of holomorphy in , N≥ 2, whose envelope of holomorphy is not diffeomorphic to a domain in .
Alessandro Perotti (1986)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Viene studiata l'equazione per le forme regolari sulla chiusura dell'intersezione di domini pseudoconvessi. Si costruisce un operatore soluzione in forma integrale e sotto ipotesi opportune si ottengono stime della soluzione nelle norme .
Ahmed Aberqi, Jaouad Bennouna, M. Hammoumi, Mounir Mekkour, Ahmed Youssfi (2014)
Applicationes Mathematicae
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We investigate the existence of renormalized solutions for some nonlinear parabolic problems associated to equations of the form ⎧ in Q = Ω×(0,T), ⎨ u(x,t) = 0 on ∂Ω ×(0,T), ⎩ in Ω. with s = (N+2)/(N+p) (p-1), , τ = (N+p)/(p-1), r = (N(p-1) + p)/(N+2), and f ∈ L¹(Q).
Philippe Souplet, Slim Tayachi (2001)
Colloquium Mathematicae
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Consider the nonlinear heat equation (E): . We prove that for a large class of radial, positive, nonglobal solutions of (E), one has the blowup estimates . Also, as an application of our method, we obtain the same upper estimate if u only satisfies the nonlinear parabolic inequality . More general inequalities of the form with, for instance, are also treated. Our results show that for solutions of the parabolic inequality, one has essentially the same estimates as for solutions...
M. Sango (2003)
Colloquium Mathematicae
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We study the initial boundary value problem for the system of thermoelasticity in a sequence of perforated cylindrical domains , s = 1,2,... We prove that as s → ∞, the solution of the problem converges in appropriate topologies to the solution of a limit initial boundary value problem of the same type but containing some additional terms which are expressed in terms of quantities related to the geometry of . We give an explicit construction of that limit problem.
A. Aytuna, A. Rashkovskii, V. Zahariuta (2002)
Annales Polonici Mathematici
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For complete Reinhardt pairs “compact set - domain” K ⊂ D in ℂⁿ, we prove Zahariuta’s conjecture about the exact asymptotics , s → ∞, for the Kolmogorov widths of the compact set in C(K) consisting of all analytic functions in D with moduli not exceeding 1 in D, τ(K,D) being the condenser pluricapacity of K with respect to D.
Wojciech M. Zajączkowski
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CONTENTS1. Introduction.......................................................................52. Notation and auxiliary results............................................93. Statement of the problem (1.1)-(1.3)..............................204. The problem (3.14).........................................................225. Auxiliary results in ...............................................346. Existence of solutions of (3.14) in ............417. Green function................................................................528....
Anne-Laure Dalibard (2011)
Journal of the European Mathematical Society
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This article investigates the long-time behaviour of parabolic scalar conservation laws of the type , where and the flux is periodic in . More specifically, we consider the case when the initial data is an disturbance of a stationary periodic solution. We show, under polynomial growth assumptions on the flux, that the difference between u and the stationary solution behaves in norm like a self-similar profile for large times. The proof uses a time and space change of variables...
M. Guedda (2002)
Colloquium Mathematicae
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We study the absence of nonnegative global solutions to parabolic inequalities of the type , where , 0 < β ≤ 2, is the β/2 fractional power of the Laplacian. We give a sufficient condition which implies that the only global solution is trivial if p > 1 is small. Among other properties, we derive a necessary condition for the existence of local and global nonnegative solutions to the above problem for the function V satisfying , where a ≥ 0, b > 0, p > 1 and V₊(x): = maxV(x),0....
P. Besala (1971)
Annales Polonici Mathematici
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Paweł Goldstein (2008)
Colloquium Mathematicae
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Convergence of global solutions to stationary solutions for a class of degenerate parabolic systems related to the p-Laplacian operator is proved. A similar result is obtained for a variable exponent p. In the case of p constant, the convergence is proved to be , and in the variable exponent case, L² and -weak.
Daniel Wachsmuth (2016)
Commentationes Mathematicae Universitatis Carolinae
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Let with be given. Then we show by means of a counter-example that the positive part of has less regularity, in particular it holds in general. Nevertheless, satisfies an integration-by-parts formula, which can be used to prove non-negativity of weak solutions of parabolic equations.
Ludwik Byszewski (1990)
Annales Polonici Mathematici
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Yūki Naito (2006)
Banach Center Publications
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We consider a nonlinear parabolic system modelling chemotaxis , in ℝ², t > 0. We first prove the existence of time-global solutions, including self-similar solutions, for small initial data, and then show the asymptotically self-similar behavior for a class of general solutions.
Christer O. Kiselman (2015)
Banach Center Publications
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A bounded open set with boundary of class C¹ which is locally weakly lineally convex is weakly lineally convex, but, as shown by Yuriĭ Zelinskiĭ, this is not true for unbounded domains. The purpose here is to construct explicit examples, Hartogs domains, showing this. Their boundary can have regularity or . Obstructions to constructing smoothly bounded domains with certain homogeneity properties will be discussed.
J. W. Cholewa, T. Dłotko (2003)
Banach Center Publications
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An abstract semilinear parabolic equation in a Banach space X is considered. Under general assumptions on nonlinearity this problem is shown to generate a bounded dissipative semigroup on . This semigroup possesses an -global attractor that is closed, bounded, invariant in , and attracts bounded subsets of in a ’weaker’ topology of an auxiliary Banach space Z. The abstract approach is finally applied to the scalar parabolic equation in Rⁿ and to the partly dissipative system. ...
Peter Pflug, Włodzimierz Zwonek (2002)
Studia Mathematica
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We give a characterization of -domains of holomorphy with the help of the boundary behavior of the Bergman kernel and geometric properties of the boundary, respectively.