On the initial value problem for a partial differential equation with operator coefficients

Mahmoud M. El-Borai

International Journal of Mathematics and Mathematical Sciences, 1980, vol. 3, 1-9

Abstract:

In the present work it is studied the initial value problem for an equation of the form L ∂ k u ∂ t k = ∑ j = 1 k L j ∂ k − j u ∂ t k − j , where L is an elliptic partial differential operator and ( L j : j = 1 , … , k ) is a family of partial differential operators with bounded operator coefficients in a suitable function space. It is found a suitable formula for solution. The correct formulation of the Cauchy problem for this equation is also studied.

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:267936

DOI: 10.1155/S0161171280000075

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