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Some Nonlinear Evolution Equations

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Part of the Applied Mathematical Sciences book series (AMS,volume 44)

Abstract

In this section we will study the following semilinear initial value problem:

$$\left\{ {\begin{array}{*{20}{c}} {\frac{{du(t)}}{{dt}} + Au(t) = f(t,u(t)), t > {{t}_{0}}} \hfill \\ {u({{t}_{0}}) = {{u}_{0}}} \hfill \\ \end{array} } \right.$$
(1.1)

where -A is the infinitesimal generator of a C0semigroup T(t), t ≥ 0, on a Banach space X and f: [t 0 ,T] X X→ X is continuous in t and satisfies a Lipschitz condition in u.

Keywords

  • Banach Space
  • Classical Solution
  • Strong Solution
  • Mild Solution
  • Nonlinear Evolution Equation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1983 Springer-Verlag New York, Inc.

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Pazy, A. (1983). Some Nonlinear Evolution Equations. In: Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, vol 44. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5561-1_6

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  • DOI: https://doi.org/10.1007/978-1-4612-5561-1_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-5563-5

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