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Decay rates of Volterra equations on ℝN

100%

Conti M., Gatti S., Pata V.

Open Mathematics

2007

tom 5

nr 4

720-732

This note is concerned with the linear Volterra equation of hyperbolic type $$\partial _{tt} u(t) - \alpha \Delta u(t) + \int_0^t {\mu (s)\Delta u(t - s)} ds = 0$$ on the whole space ℝN. New results concerning the decay of the associated energy as time goes to infinity were established.

Existence and uniqueness of solutions to weakly singular integral-algebraic and integro-differential equations

100%

Bulatov M., Lima P., Weinmüller E.

Open Mathematics

2014

tom 12

nr 2

308-321

We consider systems of integral-algebraic and integro-differential equations with weakly singular kernels. Although these problem classes are not in the focus of the main stream literature, they are interesting, not only in their own right, but also because they may arise from the analysis of certain classes of differential-algebraic systems of partial differential equations. In the first part of the paper, we deal with two-dimensional integral-algebraic equations. Next, we analyze Volterra integral equations of the first kind in which the determinant of the kernel matrix k(t, x) vanishes when t = x. Finally, the third part of the work is devoted to the analysis of degenerate integro-differential systems. The aim of the paper is to specify conditions which are sufficient for the existence of a unique continuous solution to the above problems. Theoretical findings are illustrated by a number of examples.

Ograniczanie wyników

2 Open Mathematics

1 Bulatov M.

1 Conti M.

1 Gatti S.

1 Lima P.

1 Pata V.

1 Weinmüller E.

1 2014

1 2007

Wyniki wyszukiwania

Decay rates of Volterra equations on ℝN

Existence and uniqueness of solutions to weakly singular integral-algebraic and integro-differential equations