A generalization of d'Alembert formula

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dc.creatorChang, Yu-Hsien
dc.creatorHong, Cheng-Hong
dc.date2007-09-21
dc.date.accessioned2026-07-07T08:31:24Z
dc.date.available2026-07-07T08:31:24Z
dc.descriptionIn this paper we find a closed form of the solution for the factored inhomogeneous linear equation \begin{equation*} \prod_{j=1}^{n}(\frac{\hbox{d}}{\hbox{d}t}-A_{j}) u(t) =f(t). \end{equation*} Under the hypothesis $A_{1},A_{2}, ..., A_{n}$ are infinitesimal generators of mutually commuting strongly continuous semigroups of bounded linear operators on a Banach space $X$. Here we do not assume that $A_{j}$s are distinct and we offer the computational method to get explicit solutions of certain partial differential equations.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/0709.3348
dc.identifierhttp://arxiv.org/abs/0709.3348
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138492
dc.subjectAnalysis of PDEs
dc.subject35
dc.titleA generalization of d'Alembert formula
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