Mild solution of an abstract Cauchy problem

A mild solution need only be continuous and satisfy the integrated semigroup formula. It need not lie in the generator domain or be differentiable.

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- Variation-of-constants formula Mild solution of an abstract Cauchy problem

Variation-of-constants formula

If

A

generates

U (t)

, the variation-of-constants formula is

Z (t) = U (t) Z_{0} + \int_{0}^{t} U (t - s) F (s) d s .

It is also called Duhamel's formula.

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Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 319 / 1 / h / Solution
Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 319 / 1 / e / Solution

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