Pseudosolution of an integral convolution equation of the first kind.
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| Title: | Pseudosolution of an integral convolution equation of the first kind. |
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| Authors: | Yengibaryan, N. B.1 (AUTHOR) yengib@instmath.sci.am |
| Source: | Theoretical & Mathematical Physics. May2025, Vol. 223 Issue 2, p872-877. 6p. |
| Subjects: | Absolute continuity, Integral equations, Equations |
| Abstract: | We consider the equation , where and the functions and and their first derivatives are absolutely continuous on and . An arbitrary term is added to the right-hand side of the equation. The obtained family of equations is reduced by double differentiation to an equation of the second kind. In the case of its unique solvability in , the solution is called a -pseudosolution of the original equation. We introduce the partial regularization of the equation and present some cases of the existence of a -pseudosolution. We propose a criterion for the suitability of as an approximate solution. The problem of constructing a pseudosolution of an equation on the half-line is discussed. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | We consider the equation , where and the functions and and their first derivatives are absolutely continuous on and . An arbitrary term is added to the right-hand side of the equation. The obtained family of equations is reduced by double differentiation to an equation of the second kind. In the case of its unique solvability in , the solution is called a -pseudosolution of the original equation. We introduce the partial regularization of the equation and present some cases of the existence of a -pseudosolution. We propose a criterion for the suitability of as an approximate solution. The problem of constructing a pseudosolution of an equation on the half-line is discussed. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 00405779 |
| DOI: | 10.1134/S0040577925050113 |
