Well-posedness of parabolic differential and difference equations

WELL- POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS

Nonlocal Boundary Value Problems for Elliptic-Parabolic Differential and Difference Equations

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 el...

Well-Posedness of Parabolic Differential and Difference Equations with the Fractional Differential Operator

The stable difference scheme for the approximate solution of the initial value problem du(t) dt + D 1 2 t u(t) + Au(t) = f(t), 0 < t < 1, u(0) = 0 for the differential equation in a Banach space E with the strongly positive operator A and fractional operator D 1 2 t is presented. The well-posedness of the difference scheme in difference analogues of spaces of smooth functions is established. In...

On Bitsadze-Samarskii type nonlocal boundary value problems for elliptic differential and difference equations: Well-posedness

Keywords: Elliptic equations Nonlocal boundary value problems Difference schemes Stability a b s t r a c t The well-posedness of the Bitsadze–Samarskii type nonlocal boundary value problem in Hölder spaces with a weight is established. The coercivity inequalities for the solution of the nonlocal boundary value problem for elliptic equations are obtained. The stable second order of accuracy diff...

Well-Posedness of the Boundary Value Problem for Parabolic Equations in Difference Analogues of Spaces of Smooth Functions

The first and second orders of accuracy difference schemes for the approximate solutions of the nonlocal boundary value problem v ′ (t) +Av(t) = f (t) (0 ≤ t ≤ 1), v(0) = v(λ) + μ, 0 < λ ≤ 1, for differential equation in an arbitrary Banach space E with the strongly positive operator A are considered. The well-posedness of these difference schemes in difference analogues of spaces of smooth fun...