Well-posedness of difference elliptic equation

Local Well-posedness for Hyperbolic-elliptic Ishimori Equation

In this paper we consider the hyperbolic-elliptic Ishimori initial-value problem with the form:    ∂ts = s× xs+ b(φx1sx2 + φx2sx1) on R 2 × [−1, 1]; ∆φ = 2s · (sx1 × sx2) s(0) = s0 where s(·, t) : R → S ⊂ R, × denotes the wedge product in R, x = ∂ x1 −∂ 2 x2 , b ∈ R. We prove that such system is locally well-posed for small data s0 ∈ H0 Q (R ; S), σ0 > 3/2, Q ∈ S. The new ingredient is that ...

A note on the well-posedness of the nonlocal boundary value problem for elliptic difference equations

The nonlocal boundary value problem for elliptic difference equations in an arbitrary Banach space is considered. The well-posedness of this problem is investigated. The stability, almost coercive stability and coercive stability estimates for the solutions of difference schemes of the second order of accuracy for the approximate solutions of the nonlocal boundary value problem for elliptic equ...

The Well-posedness Ofthe Kuramoto-sivashinsky Equation

The Kuramoto-Sivashinsky equation arises in a variety of applications, among which are modeling reaction-diffusion systems, flame-propagation and viscous flow problems. It is considered here, as a prototype to the larger class of generalized Burgers equations: those consist of quadratic nonlinearity and arbitrary linear parabolic part. We show that such equations are well-posed, thus admitting ...

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 ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS