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

• Autorzy: Mikhail Bulatov , Pedro Lima , Ewa Weinmüller
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Weakly singular; Two-dimensional Volterra integral-algebraic equations; Integro-differential equations

Kategorie tematyczne

• 45F15: Systems of singular linear integral equations
• 65R20: Integral equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 2
• Strony: 308-321

Daty

wydano

2014-02-01

online

2013-11-21

Twórcy

autor

Mikhail Bulatov

autor

Pedro Lima

• Universidade Técnica de Lisboa

autor

Ewa Weinmüller

• Vienna University of Technology

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0334-5