JournalszaaVol. 16, No. 4pp. 961–978

On a Theorem by W. von Wahl

  • M. Uiterdijk

    Delft University of Technology, Netherlands
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Abstract

Let AA be the - not necessarily densely defined - generator of an analytic semigroup acting in some Banach space XX. In the paper we prove a general theorem about the existence and uniqueness of solutions of

u(t)=Au(t)+F(u(t))u’(t) = Au(t) + F(u(t))
u(0)=u0.u(0) = u_0.

Our main assumption with respect to the non-linearity is that FF is locally Lipschitz continuous with respect to certain intermediate spaces between D(A)\mathcal D(A) and XX. Our theorem extends results obtained by W. von Wahl [9] and A. Lunardi [2]. In the second part this theorem is applied to the Cahn-Hilliard equation with Dirichlet boundary conditions.

Cite this article

M. Uiterdijk, On a Theorem by W. von Wahl. Z. Anal. Anwend. 16 (1997), no. 4, pp. 961–978

DOI 10.4171/ZAA/799