Well-posedness of difference scheme for elliptic-parabolic equations in Hölder spaces without a weight

2014 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Okan Gercek ◽  
Emel Zusi
Keyword(s):  
Difference Scheme ◽  
Parabolic Equations ◽  
Well Posedness ◽  
Hölder Spaces ◽  
Holder Spaces

scholarly journals On the Second Order of Accuracy Stable Implicit Difference Scheme for Elliptic-Parabolic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Allaberen Ashyralyev ◽  
Okan Gercek
Keyword(s):  
Difference Scheme ◽  
Parabolic Equations ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Approximate Solutions ◽  
Second Order ◽  
Well Posedness ◽  
Parabolic Differential Equations ◽  
Implicit Difference Scheme ◽  
Order Of Accuracy

We are interested in studying a second order of accuracy implicit difference scheme for the solution of the elliptic-parabolic equation with the nonlocal boundary condition. Well-posedness of this difference scheme is established. In an application, coercivity estimates in Hölder norms for approximate solutions of multipoint nonlocal boundary value problems for elliptic-parabolic differential equations are obtained.

scholarly journals Well Posedness for a Class of Flexible Structure in Hölder Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Claudio Cuevas ◽  
Carlos Lizama
Keyword(s):  
Boundary Conditions ◽  
External Force ◽  
Dirichlet Boundary ◽  
Flexible Structures ◽  
Dirichlet Boundary Conditions ◽  
Flexible Structure ◽  
Well Posedness ◽  
Hölder Spaces ◽  
Holder Spaces ◽  
Well Posed

We characterize well-posedness in Hölder spaces for an abstract version of the equation(∗) u′′+λu′′′=c2(Δu+μΔu′)+fwhich model thevibrationsof flexible structures possessing internal material damping and external forcef. As a consequence, we show that in case of the Laplacian with Dirichlet boundary conditions, equation(∗)is always well-posed provided0<λ<μ.

Sign in / Sign up

Export Citation Format

Share Document