Finite-dimensional Pullback Attractors for Non-autonomous Newton-Boussinesq Equations in Some Two-dimensional Unbounded Domains

Cung The Anh; Dang Thanh Son

Displaying similar documents to “Finite-dimensional Pullback Attractors for Non-autonomous Newton-Boussinesq Equations in Some Two-dimensional Unbounded Domains”

Inexact Newton-type method for solving large-scale absolute value equation $A x - | x | = b$

Jingyong Tang (2024)

Applications of Mathematics

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Newton-type methods have been successfully applied to solve the absolute value equation $A x - | x | = b$ (denoted by AVE). This class of methods usually solves a system of linear equations exactly in each iteration. However, for large-scale AVEs, solving the corresponding system exactly may be expensive. In this paper, we propose an inexact Newton-type method for solving the AVE. In each iteration, the proposed method solves the corresponding system only approximately. Moreover, it adopts a new line...

New quasi-Newton method for solving systems of nonlinear equations

Ladislav Lukšan, Jan Vlček (2017)

Applications of Mathematics

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We propose a new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR or LU decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires $O (n^{2})$ arithmetic operations per iteration in contrast with the Newton method, which requires $O (n^{3})$ operations per iteration. Computational experiments confirm the...

Newton polygons and the Łojasiewicz exponent of a holomorphic mapping of $C^{2}$

Arkadiusz Płoski (1990)

Annales Polonici Mathematici

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Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations

Monnanda Erappa Shobha, Ioannis K. Argyros, Santhosh George (2014)

Applicationes Mathematicae

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We use a combination of modified Newton method and Tikhonov regularization to obtain a stable approximate solution for nonlinear ill-posed Hammerstein-type operator equations KF(x) = y. It is assumed that the available data is $y^{δ}$ with $| | y - y^{δ} | | \leq δ$ , K: Z → Y is a bounded linear operator and F: X → Z is a nonlinear operator where X,Y,Z are Hilbert spaces. Two cases of F are considered: where $F^{'} {(x ₀)}^{- 1}$ exists (F’(x₀) is the Fréchet derivative of F at an initial guess x₀) and where F is a monotone operator....

A global analysis of Newton iterations for determining turning points

Vladimír Janovský, Viktor Seige (1993)

Applications of Mathematics

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The global convergence of a direct method for determining turning (limit) points of a parameter-dependent mapping is analysed. It is assumed that the relevant extended system has a singular root for a special parameter value. The singular root is clasified as a $b i f u r c a t i o n s i n g u l a r i t y$ (i.e., as a $d e g e n e r a t e$ turning point). Then, the Theorz for Imperfect Bifurcation offers a particular scenario for the split of the singular root into a finite number of regular roots (turning points) due to a given parameter imperfection....

Newton’s method over global height fields

Xander Faber, Adam Towsley (2014)

Journal de Théorie des Nombres de Bordeaux

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For any field $K$ equipped with a set of pairwise inequivalent absolute values satisfying a product formula, we completely describe the conditions under which Newton’s method applied to a squarefree polynomial $f \in K [x]$ will succeed in finding some root of $f$ in the $v$ -adic topology for infinitely many places $v$ of $K$ . Furthermore, we show that if $K$ is a finite extension of the rationals or of the rational function field over a finite field, then the Newton approximation sequence fails to converge...

On the Newton partially flat minimal resistance body type problems

M. Comte, Jesus Ildefonso Díaz (2005)

Journal of the European Mathematical Society

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We study the flat region of stationary points of the functional $\int_{Ω} F (| \nabla u (x) |) d x$ under the constraint $u \leq M$ , where $Ω$ is a bounded domain in $ℝ^{2}$ . Here $F (s)$ is a function which is concave for $s$ small and convex for $s$ large, and $M > 0$ is a given constant. The problem generalizes the classical minimal resistance body problems considered by Newton. We construct a family of partially flat radial solutions to the associated stationary problem when $Ω$ is a ball. We also analyze some other qualitative properties. Moreover,...

The index of analytic vector fields and Newton polyhedra

Carles Bivià-Ausina (2003)

Fundamenta Mathematicae

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We prove that if f:(ℝⁿ,0) → (ℝⁿ,0) is an analytic map germ such that $f^{- 1} (0) = 0$ and f satisfies a certain non-degeneracy condition with respect to a Newton polyhedron Γ₊ ⊆ ℝⁿ, then the index of f only depends on the principal parts of f with respect to the compact faces of Γ₊. In particular, we obtain a known result on the index of semi-weighted-homogeneous map germs. We also discuss non-degenerate vector fields in the sense of Khovanskiĭand special applications of our results to planar analytic...

A modified limited-memory BNS method for unconstrained minimization derived from the conjugate directions idea

Vlček, Jan, Lukšan, Ladislav

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A modification of the limited-memory variable metric BNS method for large scale unconstrained optimization of the differentiable function $f : ℛ^{N} \to ℛ$ is considered, which consists in corrections (based on the idea of conjugate directions) of difference vectors for better satisfaction of the previous quasi-Newton conditions. In comparison with [11], more previous iterations can be utilized here. For quadratic objective functions, the improvement of convergence is the best one in some sense, all...

Exponential polynomial inequalities and monomial sum inequalities in $p$ -Newton sequences

Charles R. Johnson, Carlos Marijuán, Miriam Pisonero, Michael Yeh (2016)

Czechoslovak Mathematical Journal

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We consider inequalities between sums of monomials that hold for all p-Newton sequences. This continues recent work in which inequalities between sums of two, two-term monomials were combinatorially characterized (via the indices involved). Our focus is on the case of sums of three, two-term monomials, but this is very much more complicated. We develop and use a theory of exponential polynomial inequalities to give a sufficient condition for general monomial sum inequalities, and use...

Canonical mappings in $Σ_{M} (D)$

Z. Abdul-Hadi, D. Bschouty, W. Hengartner (1985)

Matematički Vesnik

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On n-circled $ℋ^{\infty}$ -domains of holomorphy

Marek Jarnicki, Peter Pflug (1997)

Annales Polonici Mathematici

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We present various characterizations of n-circled domains of holomorphy $G \subset ℂ^{n}$ with respect to some subspaces of $ℋ^{\infty} (G)$ .

Balanced domains of holomorphy of type $H^{α}$

J. Siciak (1985)

Matematički Vesnik

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On the paradox of two $R_{1}, R_{2}$ domains in Schwarzschild exterior solution

A. Zięba (1972)

Colloquium Mathematicae

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Analytical View of Sir Isaac Newton's Principia

Henry Brougham, Edward John Routh

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On the Singularities of the Newtonian two dimensional N-body Problem

Carlo Marchioro, Mario Pulvirenti (1983)

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

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Si considera un sistema bidimensionale di $N$ particelle interagenti tramite un potenziale di Newton o di Coulomb e si mostra che l’insieme delle condizioni iniziali che in un tempo finito possono condurre a delle singolarità possiede misura di Lebesgue nulla.