×

Behavior of solutions to one-dimensional two-phase Stefan problems with dynamic boundary conditions. (English) Zbl 0875.35154

Kawarada, H. (ed.) et al., Proceedings of the international conference on nonlinear mathematical problems in industry, held at Iwaki Meisei University, Iwaki, Japan, during Nov. 9-13, 1992. II. Tokyo: Gakkōtosho, GAKUTO Int. Ser., Math. Sci. Appl. 2, 547-570 (1993).
Summary: We consider the behavior of solutions to one-dimensional two-phase Stefan problems for a class of nonlinear parabolic equations with dynamic boundary conditions, that is, with boundary conditions containing time derivatives on the fixed boundary. In this paper, we investigate the behavior of free boundaries in the maximal interval of existence of the solution by energy estimates for the solution.
For the entire collection see [Zbl 0830.00022].

MSC:

35R35 Free boundary problems for PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35K55 Nonlinear parabolic equations
PDFBibTeX XMLCite