An Energy Inequality and Its Applications of Nonlocal Boundary Conditions of Mixed Problem for Singular Parabolic Equations in Nonclassical Function Spaces. (10th September 2012) - Djibibe, Moussa Zakari; Tcharie, Kokou; Yurchuk, N. Iossifovich
Abstract : 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 ) / x 2 ) ( ∂ / ∂ x ) ( x 2 ∂ 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, ∫ 0 ℓ x 3 v ( x, t ) d x = 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.