Structure of Solutions to Linear Evolution Equations: Extensions of d'Alembert's Formula
Copyright policy )Structure of Solutions to Linear Evolution Equations: Extensions of d'Alembert's Formula
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.
- Alma Mater Studiorum University of Bologna Italy
- Louisiana State University United States
linear evolution equations, Linear differential equations in abstract spaces, Applied Mathematics, d'Alembert formula, Operator sine and cosine functions and higher-order Cauchy problems, Analysis, nonautonomous and inhomogeneous equations
linear evolution equations, Linear differential equations in abstract spaces, Applied Mathematics, d'Alembert formula, Operator sine and cosine functions and higher-order Cauchy problems, Analysis, nonautonomous and inhomogeneous equations
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