Necessary and Sufficient Condition of Existence for the Quadrature Surfaces Free Boundary Problem
نویسندگان
چکیده
منابع مشابه
Necessary and Sufficient Condition of Existence for the Quadrature Surfaces Free Boundary Problem
Performing the shape derivative (Sokolowski and Zolesio, 1992) and using the maximum principle, we show that the so-called Quadrature Surfaces free boundary problem QS ( f , k) ⎪⎪⎪⎨⎪⎪⎪⎩ −ΔuΩ = f in Ω uΩ = 0 on ∂Ω |∇uΩ| = k (constant) on ∂Ω. has a solution which contains strictly the support of f if and only if ∫
متن کاملA NECESSARY AND SUFFICIENT CONDITION FOR THE EXISTENCE Of A UNIQUE SOLUTION OF A DISCRETE BOUNDARY VALUE PROBLEM
A kth-order linear difference equation with constant coefficients subject to boundary conditions is considered. A necessary and sufficient condition for the existence of a unique solution for such a boundary value problem is established. The condition established answers a fundamental question for well-posedness and can be easily applied using a simple and computationally tractable algorithm th...
متن کاملA Necessary and Sufficient Condition for Deadlock-Free Wormhole Routing
An important open problem in wormhole routing has been to find a necessary and sufficient condition for deadlock-free adaptive routing. Recently, Duato has solved this problem for a restricted class of adaptive routing algorithms. In this paper, a necessary and sufficient condition is proposed that can be used for any adaptive or nonadaptive routing algorithm for wormhole routing, as long as on...
متن کاملNecessary and Sufficient Condition for Existence and Uniqueness of the Solution of Cauchy Problem for Holomorphic Fuchsian Operators
In this paper a Cauchy problem for holomorphic differential operators of Fuchsian type is investigated. Using Ovcyannikov techniques and the method of majorants, a necessary and sufficient condition for existence and uniqueness of the solution of the problem under consideration is shown.
متن کاملA necessary and sufficient condition for the existence of symmetric positive solutions of higher-order boundary value problems
where n≥ is an integer, f : (, )× (,∞)→ [,∞) is continuous, αi, βi are nonnegative constants, α i + αiβi > , i = , . . . ,n. f (t,u) may be singular at u = , t = (and/or t = ). If a function u : [, ]→ R is continuous and satisfies u(t) = u( – t) for t ∈ [, ], then we say that u(t) is symmetric on [, ]. By a symmetric positive solution of BVP (.) we mean a symmetric functi...
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: Journal of Mathematics Research
سال: 2010
ISSN: 1916-9809,1916-9795
DOI: 10.5539/jmr.v2n4p93