scholarly journals A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems

2006 ◽  
Vol 2006 ◽  
pp. 1-8 ◽  
Author(s):  
M. Denche ◽  
S. Djezzar
Keyword(s):  
Boundary Value ◽  
Boundary Value Method ◽  
Ill Posed

scholarly journals A modified quasi-boundary value method for an abstract ill-posed biparabolic problem

2017 ◽  
Vol 15 (1) ◽  
pp. 1649-1666 ◽  
Author(s):  
Khelili Besma ◽  
Boussetila Nadjib ◽  
Rebbani Faouzia
Keyword(s):  
Original Problem ◽  
Convergence Rates ◽  
Boundary Value ◽  
A Priori ◽  
Numerical Tests ◽  
Convergence Results ◽  
A Priori Bound ◽  
Boundary Value Method ◽  
Ill Posed ◽  
Stable Solutions

Abstract In this paper, we are concerned with the problem of approximating a solution of an ill-posed biparabolic problem in the abstract setting. In order to overcome the instability of the original problem, we propose a modified quasi-boundary value method to construct approximate stable solutions for the original ill-posed boundary value problem. Finally, some other convergence results including some explicit convergence rates are also established under a priori bound assumptions on the exact solution. Moreover, numerical tests are presented to illustrate the accuracy and efficiency of this method.

scholarly journals Sufficient conditions for hyperbolicity and consistency of the dynamic equations for fluid-saturated solids

2021 ◽  
Author(s):  
Vladimir A. Osinov
Keyword(s):  
Boundary Value Problem ◽  
Wave Speed ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Positive Definiteness ◽  
Dynamic Equations ◽  
Necessary Condition ◽  
Systems Of Equations ◽  
Acoustic Tensor ◽  
Ill Posed

AbstractPrevious studies showed that the dynamic equations for a porous fluid-saturated solid may lose hyperbolicity and thus render the boundary-value problem ill-posed while the equations for the same but dry solid remain hyperbolic. This paper presents sufficient conditions for hyperbolicity in both dry and saturated states. Fluid-saturated solids are described by two different systems of equations depending on whether the permeability is zero or nonzero (locally undrained and drained conditions, respectively). The paper also introduces a notion of wave speed consistency between the two systems as a necessary condition which must be satisfied in order for the solution in the locally drained case to tend to the undrained solution as the permeability tends to zero. It is shown that the symmetry and positive definiteness of the acoustic tensor of the skeleton guarantee both hyperbolicity and the wave speed consistency of the equations.

Sign in / Sign up

Export Citation Format

Share Document