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Zbl 0996.35027
Ashyralyev, A.; Hanalyev, A.; Sobolevskii, P.E.
(Sobolevskij, P.E.)
Coercive solvability of the nonlocal boundary value problem for parabolic differential equations.
(English)
[J] Abstr. Appl. Anal. 6, No.1, 53-61 (2001). ISSN 1085-3375; ISSN 1687-0409/e

Summary: The nonlocal boundary value problem, $v'(t) + Av(t) = f(t)$ $(0 \leq t \leq 1)$, $v(0) = v(\lambda) + \mu$ $(0 < \lambda \leq 1)$, 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 $\{0 \leq t \leq 1$, $x \in {\Bbb{R}}^n\}$ for $2m$-order multidimensional parabolic equations are obtained.
MSC 2000:
*35K35 Higher order parabolic equations, boundary value problems
47J35 Nonlinear evolution equations
35K90 Abstract parabolic evolution equations

Keywords: coercive stability estimates; Schauder's estimates in Hölder norms

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