“Bonnes solutions” d’un problème d’évolution semi-linéaire. (“Mild solutions” of a semilinear evolution problem). (French) Zbl 0635.34013

Bénilan, Philippe; Crandall, Michael G.; Pazy, Amnon

C. R. Acad. Sci., Paris, Sér. I 306, No. 13, 527-530 (1988).

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