Structure of solutions to linear evolution equations: Extensions of d'Alembert's formula (Q1922917)
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scientific article; zbMATH DE number 930176
| Language | Label | Description | Also known as |
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| English | Structure of solutions to linear evolution equations: Extensions of d'Alembert's formula |
scientific article; zbMATH DE number 930176 |
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Structure of solutions to linear evolution equations: Extensions of d'Alembert's formula (English)
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13 May 1997
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The authors start from a factored equation \(\prod^N_{j=1} ({d\over dt}- A_j)u(t)=0\) with commuting generators \(A_j\) and the corresponding d'Alembert formula for the solutions \(u(t)= \sum^N_{j=1} e^{tA_j}x_j\). They find the appropriate generalization in the case of nonautonomous and inhomogeneous equations. Interesting examples are given.
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linear evolution equations
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d'Alembert formula
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nonautonomous and inhomogeneous equations
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