## Nonlinear evolution equations and product stable operators on Banach spaces

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- by G. F. Webb
- Trans. Amer. Math. Soc.
**155**(1971), 409-426 - DOI: https://doi.org/10.1090/S0002-9947-1971-0276842-9
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## Abstract:

The method of product integration is used to obtain solutions to the time dependent Banach space differential equation $u’(t) = A(t)(u(t)),t \geqq 0$, where $A$ is a function from $[0,\infty )$ to the set of nonlinear operators from the Banach space $X$ to itself and $u$ is a function from $[0,\infty )$ to $X$. The main requirements placed on $A$ are that $A$ is $m$-dissipative and product stable on its domain. Applications are given to a linear partial differential equation, to nonlinear dissipative operators in Hilbert space, and to continuous, $m$-dissipative, everywhere defined operators in Banach spaces.## References

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## Bibliographic Information

- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**155**(1971), 409-426 - MSC: Primary 47.80
- DOI: https://doi.org/10.1090/S0002-9947-1971-0276842-9
- MathSciNet review: 0276842