×

Uniqueness of the solution to a nonlinear system arising in phase transition. (English) Zbl 0873.35040

Kenmochi, N. (ed.) et al., Proceedings of the Banach Center minisemester on nonlinear analysis and applications, Warsaw, Poland, November 14 – December 15, 1994. Tokyo: Gakkōtosho Co., Ltd. GAKUTO Int. Ser., Math. Sci. Appl. 7, 261-271 (1995).
This paper deals with a class of initial-boundary value problems for nonlinear systems of parabolic PDEs, which covers some non-isothermal models for diffusive phase transition in higher space dimensions. A uniqueness result is established, and the continuous dependence upon the data is shown; the proof is based on the theory of subdifferentials of convex functions.
For the entire collection see [Zbl 0853.00039].
Reviewer: M.A.Vivaldi (Roma)

MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
49J20 Existence theories for optimal control problems involving partial differential equations
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
PDF BibTeX XML Cite