A generalization of d'Alembert formula

Yu Hsien Chang, Cheng Hong Hong

Research output: Contribution to journalArticle

Abstract

In this paper we find a closed form of the solution for the factored inhomogeneous linear equation ∏nj=1(d/dt-a j)u(t) = f(t). Under the hypothesis A1, A 2.....An are infinitesimal generators of mutually commuting strongly continuous semigroups of bounded linear operators on a Banach space X. Here we do not assume that AjS are distinct and we offer the computational method to get explicit solutions of certain partial differential equations.

Original languageEnglish
Pages (from-to)411-427
Number of pages17
JournalProceedings of the Indian Academy of Sciences: Mathematical Sciences
Volume117
Issue number3
DOIs
Publication statusPublished - 2007 Aug 1

Keywords

  • C semigroup
  • d'Alembert formula

ASJC Scopus subject areas

  • Mathematics(all)

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