Two-phase Stefan problems for parabolic-elliptic equations
نویسندگان
چکیده
منابع مشابه
Nonlinear Two-Phase Stefan Problem
In this paper we consider a nonlinear two-phase Stefan problem in one-dimensional space. The problem is mapped into a nonlinear Volterra integral equation for the free boundary.
متن کاملElliptic and Parabolic Equations
Elliptic equations: 1. Harmonic functions 2. Perron’s method 3. Potential theory 4. Existence results; the method of suband supersolutions 5. Classical maximum principles for elliptic equations 6. More regularity, Schauder’s theory for general elliptic operators 7. The weak solution approach in one space dimension 8. Eigenfunctions for the Sturm-Liouville problem 9. Generalization to more dimen...
متن کاملEfficient Uzawa Algorithms for Two Phase Stefan Type Problems
In this paper we present and analyze Uzawa type algorithms for solving discretized variational inequalities arising from two phase Stefan type problems. For a Uzawa type algorithm and its improved version we show convergence and derive bounds on convergence rates. For the improved Uzawa algorithm, the convergence rate is shown to be uniformly bounded away from 1 if τh−2 is kept bounded, with τ ...
متن کاملSchauder Estimates for Elliptic and Parabolic Equations
The Schauder estimate for the Laplace equation was traditionally built upon the Newton potential theory. Different proofs were found later by Campanato [Ca], in which he introduced the Campanato space; Peetre [P], who used the convolution of functions; Trudinger [T], who used the mollification of functions; and Simon [Si], who used a blowup argument. Also a perturbation argument was found by Sa...
متن کاملInverse problems for parabolic equations
Let ut −∇2u = f(x) := ∑M m=1 amδ(x− xm) in D × [0,∞), where D ⊂ R3 is a bounded domain with a smooth connected boundary S, am = const, δ(x− xm) is the delta-function. Assume that u(x, 0) = 0, u = 0 on S. Given the extra data u(yk, t) := bk(t), 1 ≤ k ≤ K, can one find M,am, and xm? Here K is some number. An answer to this question and a method for finding M,am, and xm are given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1988
ISSN: 0386-2194
DOI: 10.3792/pjaa.64.377