An Energy Inequality and Its Applications of Nonlocal Boundary Conditions of Mixed Problem for Singular Parabolic Equations in Nonclassical Function Spaces

Moussa Zakari Djibibe, Kokou Tcharie, N. Iossifovich Yurchuk
2012 ISRN Applied Mathematics  
The aim of this paper is to establish a priori estimates of the following nonlocal boundary conditions mixed problem for parabolic equation: ∂v/∂t-(a(t)/x2)(∂/∂x)(x2∂v/∂x)+b(x,t)v=g(x,t), v(x, 0)=ψ(x), 0≤x≤ℓ, v(ℓ, t)=E(t), 0≤t≤T, ∫0ℓx3v(x,t)dx=G(t), 0≤t≤ℓ. It is important to know that a priori estimates established in nonclassical function spaces is a necessary tool to prove the uniqueness of a strong solution of the studied problems.
doi:10.5402/2012/138308 fatcat:xzmhxnoqjrg2jmpczavzrlilri