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.
|Number of pages||17|
|Journal||Proceedings of the Indian Academy of Sciences: Mathematical Sciences|
|Publication status||Published - 2007 Aug|
- C semigroup
- d'Alembert formula
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