A Necessary and Sufficient Condition for Global Existence for a Degenerate Parabolic Boundary Value Problem
نویسندگان
چکیده
منابع مشابه
A 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 کاملExistence of positive solutions for a boundary value problem of a nonlinear fractional differential equation
This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.
متن کاملNecessary 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 کاملExistence and uniqueness of solutions for a periodic boundary value problem
In this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in Banach spaces admitting the existence of a lower solution.
متن کاملA necessary and sufficient condition for global existence for a quasilinear reaction-diffusion system
We show that the reaction-diffusion system ut = ∆φ(u) + f (v), vt = ∆ψ(v) + g(u), with homogeneous Neumann boundary conditions, has a positive global solution on Ω× [0,∞) if and only if ∫∞ds/ f (F−1(G(s)))=∞ (or, equivalently, ∫∞ds/g(G−1(F(s)))=∞), where F(s) = ∫ s 0 f (r)dr and G(s) = ∫ s 0 g(r)dr. The domain Ω ⊆ RN (N ≥ 1) is bounded with smooth boundary. The functions φ, ψ, f , and g are non...
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 Mathematical Analysis and Applications
سال: 1998
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5900