Linear Partial Differential Equations in Module of Formal Generalized Functions over Commutative Ring
نویسندگان
چکیده
We study the Cauchy problem for linear differential equation ∂u/∂t = Fu in module of formal generalized functions over a commutative ring, where F is operator finite or infinite order. prove well-posedness problem, find its fundamental solution, and obtain representation unique solution to form convolution initial condition. These results are specified heat equation, simplest transport one-dimensional wave equation.
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ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2021
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-021-05505-0