## Abstract and Applied Analysis

### Coercive solvability of the nonlocal boundary value problem for parabolic differential equations

#### Abstract

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 $\{0\leq t\leq 1,x\in\mathbb{R}^n\}$ for $2m$-order multidimensional parabolic equations are obtaine.

#### Article information

Source
Abstr. Appl. Anal., Volume 6, Number 1 (2001), 53-61.

Dates
First available in Project Euclid: 13 April 2003

https://projecteuclid.org/euclid.aaa/1050266658

Digital Object Identifier
doi:10.1155/S1085337501000495

Mathematical Reviews number (MathSciNet)
MR1862284

Zentralblatt MATH identifier
0996.35027

Subjects
Primary: 65N 47D
Secondary: 34B

#### Citation

Ashyralyev, A.; Hanalyev, A.; Sobolevskii, P. E. Coercive solvability of the nonlocal boundary value problem for parabolic differential equations. Abstr. Appl. Anal. 6 (2001), no. 1, 53--61. doi:10.1155/S1085337501000495. https://projecteuclid.org/euclid.aaa/1050266658

#### References

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