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“Bonnes solutions” d’un problème d’évolution semi-linéaire. (“Mild solutions” of a semilinear evolution problem). (French) Zbl 0635.34013
Summary: We consider the notion of “mild solutions”, which has been introduced for general nonlinear evolution problems, in the case of the semilinear equation $$du/dt+Lu=B(u)$$, where L is any linear operator and B is a continuous operator; we obtain equivalent formulations and show that the property of time reversibility, which fails for general nonlinear problems, holds in the semilinear case.

##### MSC:
 34A34 Nonlinear ordinary differential equations and systems, general theory 34A99 General theory for ordinary differential equations
##### Keywords:
mild solutions; nonlinear evolution problems