Problem for nonhomogeneous second order evolution equation with homogeneous integral condition (Q2812884)
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scientific article; zbMATH DE number 6593015
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Problem for nonhomogeneous second order evolution equation with homogeneous integral condition |
scientific article; zbMATH DE number 6593015 |
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13 June 2016
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Stieltjes integral over measure
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partial equations
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Problem for nonhomogeneous second order evolution equation with homogeneous integral condition (English)
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The authors propose a method of solving the problem with homogeneous integral conditions for a nonhomogeneous evolution equation with an abstract operator in a Banach space \(H\). For fixed time variable, the right-hand side of the evolution equation belongs to a special subspace \(N\subseteq H\) and is represented as the Stieltjes integral over a certain measure. The solution of this problem is also represented as Stieltjes integral over the same measure. The method is applied to solve the problem with integral conditions for partial differential equations of second order in the time variable and, in the general case, for the one of infinite order in the spatial variable.
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