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Differential Equations, Vol. 40, No. 5, 2004, pp. 686–691. Translated from Differentsial’nye Uravneniya, Vol. 40, No. 5, 2004, pp. 639–644. Original Russian Text Copyright c 2004 by Baranovskaya, Yurchuk, Charie Koku. PARTIAL DIFFERENTIAL EQUATIONS A Classical Solution Weakened on the Axis for a Centrally Symmetric Mixed Problem for a Three-Dimensional Hyperbolic Equation of Even Order in Holder ¨ Spaces S. N. Baranovskaya, N. I. Yurchuk, and Charie Koku Belarus State University, Minsk, Belarus Received February 18, 2003 ¯ ¯ 1. In the cylinder Q = G × (0,T ), where G = {x ∈ R : r = |x| <R, 0 <R < ∞} is the ball 2 2 2 of radius R and |x| = x + x + x , we consider the mixed problem 1 2 3 − a ∆ u + F (u; r, t)= 0, (1) ∂t k=1 ∂ u = ϕ (r), 0 ≤ l ≤ 2m − 1, (2) ∂t t=0 ∆ u =0, 0 ≤ k ≤ m − 1, (3) which is centrally symmetric with respect to the space variables x =(x ,x ,x ). Here 1 2 3 2 2 2 2 2 2 ∆= ∂ /∂x +
Differential Equations – Springer Journals
Published: Oct 17, 2004
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