Well-Posedness of Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces without a Weight

Subject Local and nonlocal boundary value problems for partial differential equations
Title Well-Posedness of Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces without a Weight
Author(s) Allaberen Ashyralyev, Okan Gercek, Emel Zusi
Keywords Difference scheme, elliptic-parabolic equation, coercivity inequalities, well-posedness.
Abstract In the present paper, we are interested in studying a second order of accuracy difference scheme for the approximate solution of the elliptic-parabolic equation with the nonlocal boundary condition. Theorem on well-posedness of this problem in Hölder spaces without a weight is given. In an application, coercivity estimates in Hölder norms for approximate solution of a nonlocal boundary value problem for elliptic-parabolic differential equation are obtained.