A generalization of d'Alembert formula

Yu Hsien Chang; Cheng Hong Hong

doi:10.1007/s12044-007-0035-8

A generalization of d'Alembert formula

Yu Hsien Chang^*
, Cheng Hong Hong

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.....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_jS are distinct and we offer the computational method to get explicit solutions of certain partial differential equations.

Original language	English
Pages (from-to)	411-427
Number of pages	17
Journal	Proceedings of the Indian Academy of Sciences: Mathematical Sciences
Volume	117
Issue number	3
DOIs	https://doi.org/10.1007/s12044-007-0035-8
Publication status	Published - 2007 Aug

Keywords

C semigroup
d'Alembert formula

ASJC Scopus subject areas

General Mathematics

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10.1007/s12044-007-0035-8

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AB - 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.

KW - C semigroup

KW - d'Alembert formula

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A generalization of d'Alembert formula

Abstract

Keywords

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