On well-posedness of the linear Cauchy problem with the distributional right-hand side and discontinuous coefficients
| dc.creator | Kinzebulatov, Damir | |
| dc.date | 2007-09-10 | |
| dc.date | 2007-10-16 | |
| dc.date.accessioned | 2026-07-07T08:36:09Z | |
| dc.date.available | 2026-07-07T08:36:09Z | |
| dc.description | We prove the well-posedness of the Cauchy problem for the linear differential system of the form $x^{\prime}-A(t)x=f$, where $f$ is a distribution and $A$ possesses at most first-kind discontinuities together with all its derivatives defined almost everywhere. The left-hand side of this system contains the product of a distribution and, in general, a discontinuous function, which is undefined in the classical space of the distributions with the smooth test functions $\mathcal D'$, so the Cauchy problem has no solution in $\mathcal D'$. In what follows, we cosider this system in the space of distributions with the discontinuous test functions, whose elements admit continuous and associative multiplication by functions possessing at most first-kind discontinuities (together with all their derivatives defined almost everywhere), and show that there exists the unique solution of the Cauchy problem which depends continuously on $f$. | |
| dc.identifier | https://arxiv.org/abs/0709.1509 | |
| dc.identifier | http://arxiv.org/abs/0709.1509 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139971 | |
| dc.subject | Functional Analysis | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 46F10; 34A30 | |
| dc.title | On well-posedness of the linear Cauchy problem with the distributional right-hand side and discontinuous coefficients | |
| dc.type | text |