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Displaying 1021 – 1040 of 1240

The dispersion of gas exhalations and the problem of distribution of new sources on a dry hilly surface

Dien Hien Tran (1986)

Aplikace matematiky

The process of gas exhalations in the lower layer of the atmosphere and the problem of distribution of new sources of exhalations in a hilly terrain are studied. Among other, the following assumptions are introduced: (1) the terrain is a hilly one, (2) the exhalations enter a chemical reaction with the atmosphere, (3) the process is stationary, (4) the vector of wind velocity satisfies the continuity equation. The mathematical formulation of the problem then is a mixed boundary value problem for...

The dual variational principle and discontinuous elliptic problems with strong resonance at infinity.

David Arcoya, Antonio Cañada (1990)

Extracta Mathematicae

The elliptic problems in a family of planar open sets

Abdelkader Tami (2019)

Applications of Mathematics

We propose, on a model case, a new approach to classical results obtained by V. A. Kondrat'ev (1967), P. Grisvard (1972), (1985), H. Blum and R. Rannacher (1980), V. G. Maz'ya (1980), (1984), (1992), S. Nicaise (1994a), (1994b), (1994c), M. Dauge (1988), (1990), (1993a), (1993b), A. Tami (2016), and others, describing the singularities of solutions of an elliptic problem on a polygonal domain of the plane that may appear near a corner. It provides a more precise description of how the solutions...

The equation $\nabla_{2}u+a_{10}(x,y)\frac{\partial u}{\partial x}+a_{01}(x,y)\frac{\partial u% }{\partial y}+a_{00}(x,y)u=F(x,y)$ . Estimates connected to boundary value problems

Alberto Cialdea (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

. The determination of costant of (1.5) is given when existence and uniqueness hold. If $p=2$ , whatever the index, a method for computation of costant is developed.

The equation $- Δ 𝑢 - λ \frac{𝑢}{{| 𝑥 |}^{2}} = {| \nabla 𝑢 |}^{𝑝} + 𝑐 𝑓 (𝑥)$ : The optimal power

Boumediene Abdellaoui, Ireneo Peral (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We will consider the following problem $- Δ u - λ \frac{u}{{| x |}^{2}} = {| \nabla u |}^{p} + c f, u > 0 in Ω,$ where $Ω \subset ℝ^{N}$ is a domain such that $0 \in Ω$ , $N \geq 3$ , $c > 0$ and $λ > 0$ . The main objective of this note is to study the precise threshold $p_{+} = p_{+} (λ)$ for which there is novery weak supersolutionif $p \geq p_{+} (λ)$ . The optimality of $p_{+} (λ)$ is also proved by showing the solvability of the Dirichlet problem when $1 \leq p < p_{+} (λ)$ , for $c > 0$ small enough and $f \geq 0$ under some hypotheses that we will prescribe.

The existence of positive solution to some asymptotically linear elliptic equations in exterior domains.

Gongbao Li, Gao-Feng Zheng (2006)

Revista Matemática Iberoamericana

In this paper, we are concerned with the asymptotically linear elliptic problem -Δu + λ0u = f(u), u ∈ H01(Ω) in an exterior domain Ω = RnO (N ≥ 3) with O a smooth bounded and star-shaped open set, and limt→+∞ f(t)/t = l, 0 < l < +∞. Using a precise deformation lemma and algebraic topology argument, we prove under our assumptions that the problem possesses at least one positive solution.

The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements

Josef Nedoma (1979)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The finite element solution of second order elliptic problems with the Newton boundary condition

Libor Čermák (1983)

Aplikace matematiky

The convergence of the finite element solution for the second order elliptic problem in the $n$ -dimensional bounded domain $(n \geq 2)$ with the Newton boundary condition is analysed. The simplicial isoparametric elements are used. The error estimates in both the $H^{1}$ and $L_{2}$ norms are obtained.

The frequency decomposition multi-grid method. II. Convergence analysis based on the additive Schwarz method.

Wolfgang Hackbusch (1992)

Numerische Mathematik

The Frequency Decomposition Multi-Grid Method. Part I: Application to Anisotropic Equations.

Wolfgang Hackbusch (1989/1990)

Numerische Mathematik

The functional calculus for the laplacian on Lipschitz domains

David Jerison, Carlos E. Kenig (1989)

Journées équations aux dérivées partielles

The G method for heterogeneous anisotropic diffusion on general meshes

Léo Agélas, Daniele A. Di Pietro, Jérôme Droniou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In the present work we introduce a new family of cell-centered Finite Volume schemes for anisotropic and heterogeneous diffusion operators inspired by the MPFA L method. A very general framework for the convergence study of finite volume methods is provided and then used to establish the convergence of the new method. Fairly general meshes are covered and a computable sufficient criterion for coercivity is provided. In order to guarantee consistency in the presence of heterogeneous diffusivity,...

The Gauss Map for Surfaces in 4-Space.

Joel L. Weiner (1984)

Mathematische Annalen

The $h - p$ version of the boundary element method on polygonal domains with quasiuniform meshes

E. P. Stephan, M. Suri (1991)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The Hierarchical Basis Multigrid Method.

R.E. Bank, H. Yserentant, T.F. Dupont (1987/1988)

Numerische Mathematik

The hierarchical basis multigrid method for convection-diffusion equations.

R.E. Bank, M. Benbourenane (1992)

Numerische Mathematik

The index of isolated critical points and solutions of elliptic equations in the plane

G. Alessandrini, R. Magnanini (1992)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The inverse problem for elliptic equations from Dirichlet to Neumann map in multiply connected domains.

Wen, Guochun, Xu, Zuoliang, Yang, Fengmin (2009)

Boundary Value Problems [electronic only]

The $L^{p}$ -Helmholtz projection in finite cylinders

Tobias Nau (2015)

Czechoslovak Mathematical Journal

In this article we prove for $1 < p < \infty$ the existence of the $L^{p}$ -Helmholtz projection in finite cylinders $Ω$ . More precisely, $Ω$ is considered to be given as the Cartesian product of a cube and a bounded domain $V$ having $C^{1}$ -boundary. Adapting an approach of Farwig (2003), operator-valued Fourier series are used to solve a related partial periodic weak Neumann problem. By reflection techniques the weak Neumann problem in $Ω$ is solved, which implies existence and a representation of the $L^{p}$ -Helmholtz projection as...

The Lane-Emden Function and Nonlinear Eigenvalues Problems

Ould Ahmed Izid Bih Isselkou (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

We consider a semilinear elliptic eigenvalues problem on a ball of $ℜ^{n}$ and show that all the eigenfunctions and eigenvalues, can be obtained from the Lane-Emden function.

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