Abstract and Applied Analysis
Volume 6 (2001), Issue 1, Pages 53-61
doi:10.1155/S1085337501000495
Coercive solvability of the nonlocal boundary value problem for parabolic differential equations
A. Ashyralyev1
, A. Hanalyev2
and P.E. Sobolevskii3
1Department of Mathematics, Fatih University, Istanbul, Turkey
2Department of AppliedMathematics, Turkmen State University, Ashgabat, Turkmenistan
3Institute of Mathematics, Hebrew University, Jerusalem, Israel
Abstract
The nonlocal boundary value problem, v′(t)+Av(t)=f(t)(0≤t≤1),v(0)=v(λ)+μ(0<λ≤1), in an arbitrary Banach space E with the strongly positive operator A, is considered. The coercive stability estimates in Hölder norms for the solution of this problem are proved. The exact Schauder's estimates in Hölder norms of solutions of the boundary value problem on the range {0≤t≤1,xℝ n} for 2m-order multidimensional parabolic equations are obtaine.