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)


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)