Nonlocal Boundary Value Problems for Elliptic-Parabolic Differential and Difference Equations
نویسندگان
چکیده
The abstract nonlocal boundary value problem −d2u t /dt2 Au t g t , 0 < t < 1, du t /dt − Au t f t , 1 < t < 0, u 1 u −1 μ for differential equations in a Hilbert space H with the self-adjoint positive definite operator A is considered. The well-posedness of this problem in Hölder spaces with a weight is established. The coercivity inequalities for the solution of boundary value problems for elliptic-parabolic equations are obtained. The first order of accuracy difference scheme for the approximate solution of this nonlocal boundary value problem is presented. The well-posedness of this difference scheme in Hölder spaces is established. In applications, coercivity inequalities for the solution of a difference scheme for elliptic-parabolic equations are obtained.
منابع مشابه
On Bitsadze-Samarskii type nonlocal boundary value problems for elliptic differential and difference equations: Well-posedness
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