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The Rothe-Galerkin method is used for discretization. The rate of convergence in $C (I, L_{p} (G))$ for the approximate solution of a quasilinear parabolic equation with a Volterra operator on the right-hand side is established.

Error evaluation of approximate solutions for sum-difference equations in two variables.

Pachpatte, Baburao G. (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Error minimization in approximate solution of integral equations

Jaroslav Milota (1965)

Commentationes Mathematicae Universitatis Carolinae

Essential norms of the Neumann operator of the arithmetical mean

Josef Král, Dagmar Medková (2001)

Mathematica Bohemica

Let $K \subset ℝ^{m}$ ( $m \geq 2$ ) be a compact set; assume that each ball centered on the boundary $B$ of $K$ meets $K$ in a set of positive Lebesgue measure. Let $C_{0}^{(1)}$ be the class of all continuously differentiable real-valued functions with compact support in $ℝ^{m}$ and denote by $σ_{m}$ the area of the unit sphere in $ℝ^{m}$ . With each $ϕ \in C_{0}^{(1)}$ we associate the function $W_{K} ϕ (z) = \frac{1}{σ_{m}} \underset{ℝ^{m} ∖ K}{\to} \int g r a d ϕ (x) \cdot \frac{z - x}{{| z - x |}^{m}} x$ of the variable $z \in K$ (which is continuous in $K$ and harmonic in $K ∖ B$ ). $W_{K} ϕ$ depends only on the restriction ${ϕ |}_{B}$ of $ϕ$ to the boundary $B$ of $K$ . This gives rise to a linear operator $W_{K}$ acting from...

Estimates of a stabilization rate as $t \to \infty$ of solutions of a nonlinear integro-differential equation.

Jangveladze, T., Kiguradze, Z. (2002)

Georgian Mathematical Journal

Estimation for bounded solutions of integral inequalities involving infinite integration limits.

Tan, Man-Chun, Yang, En-Hao (2006)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Estimation of the condition number of a matrix in the direct discretization of the Symm equation on a quasi-uniform grid.

Voronin, V.V. (2000)

Siberian Mathematical Journal

Estimations $L^{2}$ pour les noyaux singuliers

R. Coifman, A. McIntosch, Yves Meyer (1981)

Journées équations aux dérivées partielles

Étude de l'équation de Fredholm au voisinage d'une borne critique

P. Sablonnière (1977)

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

Etude des Solutions d΄ une Classe d΄ Equatiens Integrodifferentielles Non lineaires aux Operateurs Hyperboliques Ayant Pour Limites des Fonctionnelles Integrales

D. Mangeron, L. E. Krivocheined, M. N. Oguztoreli, K. V. Leung (1975)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Étude d'une fonction remarquable associée aux moyennes de convolution

Christian Even (1999)

Annales de l'institut Fourier

Dans cet article nous étudions la série génératrice des poids alternés d’une moyenne de convolution induite par un processus de diffusion. Nous montrons que celle-ci est une fonction méromorphe, naturellement liée à un certain opérateur compact. Cette fonction est simplement égale à $d (- z) / d (z)$ , lorsque le déterminant de Fredholm $d (z)$ de cet opérateur existe, et nous la précisons dans les autres cas.

Evolution in a changing environment: existence of solutions

P. Rybka, Q. Tang, D. Waxman (2003)

Colloquium Mathematicae

We establish the existence of solutions of an intrinsically nonlinear differential-integral equation that arises from the mathematical modelling of the evolution of an asexual population in a changing environment. The main objective is to pave the way for a rigorous analysis of the linear stability of travelling wave solutions of the corresponding problem.

Exemples de noyaux admettant des resolvantes.

Hédi Ben Saad (1983)

Mathematische Annalen

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