Numerical solution of a parabolic equation with a weakly singular positive-type memory term.

Slodička, Marián

Displaying similar documents to “Numerical solution of a parabolic equation with a weakly singular positive-type memory term.”

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Resolvents, integral equations, limit sets

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In this paper we study a linear integral equation $x (t) = a (t) - \int_{0}^{t} C (t, s) x (s) d s$ , its resolvent equation $R (t, s) = C (t, s) - \int_{s}^{t} C (t, u) R (u, s) d u$ , the variation of parameters formula $x (t) = a (t) - \int_{0}^{t} R (t, s) a (s) d s$ , 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.