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Fully Nonlinear Equations by Linearization and Maximal Regularity, and Applications

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Partial Differential Equations and Functional Analysis

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 22))

Abstract

Let X and D be Banach spaces, with D continuously and densely embedded in X, and let O be an open set in D. We are concerned with the following initial value problem:

$$ \left\{ {\begin{array}{*{20}{c}} {u'(t) = F\left( {t,u(t)} \right),\;t \geqslant 0,} \\ {u(0) = {u_0},} \\ \end{array} } \right\} $$
((1.1))

where \( {u_o} \in O,F:\left[ {0, + \infty \left[ { \times O \to X,\left( {t,x} \right) \to F\left( {t,x} \right)} \right.} \right. \), is a suitable mapping.

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© 1996 Birkhäuser Boston

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Da Prato, G. (1996). Fully Nonlinear Equations by Linearization and Maximal Regularity, and Applications. In: Cea, J., Chenais, D., Geymonat, G., Lions, J.L. (eds) Partial Differential Equations and Functional Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 22. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2436-5_6

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  • DOI: https://doi.org/10.1007/978-1-4612-2436-5_6

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7536-7

  • Online ISBN: 978-1-4612-2436-5

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