The modified quasi-boundary-value method for an ill-posed generalized elliptic problem

Abstract

In this study, we are interested in the regularization of an ill-posed problem generated by a generalized elliptic equation in an abstract framework. The regularization strategy is based on the modified quasi-boundary-valued method, which allows us to construct a stable solution depending on a small parameter ε\varepsilon . To justify the theoretical results obtained, we present a few numerical examples to demonstrate the accuracy of the approximate solution and the effectiveness of the method used in our investigation.

Keywords

• ill-posed problems
• fractional elliptic equations
• regularization
• quasi-boundary-value method
• 35j25
• 35r11
• 35r30
• 35r25
• 35r30
• 47a52