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Resolvents, integral equations, limit sets

Theodore Allen Burton, D. P. Dwiggins (2010)

Mathematica Bohemica

In this paper we study a linear integral equation x ( t ) = a ( t ) - ∫ 0 t C ( t , s ) x ( s ) d s , its resolvent equation R ( t , s ) = C ( t , s ) - ∫ s t C ( t , u ) R ( u , s ) d u , the variation of parameters formula x ( t ) = a ( t ) - ∫ 0 t R ( t , s ) a ( s ) d s , and a perturbed equation. The kernel, C ( t , s ) , satisfies classical smoothness and sign conditions assumed in many real-world problems. We study the effects of perturbations of C and also the limit sets of the resolvent. These results lead us to the study of nonlinear perturbations.

Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media

Shanghui Jia, Deli Li, Tang Liu, Shu Hua Zhang (2008)

Applications of Mathematics

Asymptotic error expansions in the sense of L ∞ -norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing...

Riemann problem on the double of a multiply connected circular region

V. V. Mityushev (1997)

Annales Polonici Mathematici

The Riemann problem has been solved in [9] for an arbitrary closed Riemann surface in terms of the principal functionals. This paper is devoted to solution of the problem only for the double of a multiply connected region and can be treated as complementary to [9,1]. We obtain a complete solution of the Riemann problem in that particular case. The solution is given in analytic form by a Poincaré series.

Second order semilinear Volterra integrodifferential equation in Banach space

Jan Bochenek (1992)

Annales Polonici Mathematici

By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of some semilinear second order Volterra integrodifferential equations in Banach spaces is proved. The results are applied to some integro-partial differential equations.

Semigroup Analysis of Structured Parasite Populations

J. Z. Farkas, D. M. Green, P. Hinow (2010)

Mathematical Modelling of Natural Phenomena

Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which describes the evolution of such a population is a first-order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral...

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