Abstract
AbstractThis research studies the inverse boundary value problem for fractional elliptic equation of Tricomi–Gellerstedt–Keldysh type and obtains a condition stability result. To recover the continuous dependence of the solution on the measurement data, a generalized Tikhonov regularization method based on ill-posedness analysis is constructed. Under the a priori and a posterior selection rules for the regularization parameter, corresponding Hölder type convergence results are obtained. On this basis, this thesis verifies the simulation effect of the generalized Tikhonov method through numerical examples. The examples show that the method performs well in dealing with the problem under consideration.
Publisher
Springer Science and Business Media LLC
Reference28 articles.
1. Mathematics in Science and Engineering;I. Podlubny,1999
2. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
3. Bres, L.: Mathematical Aspects of Subsonic and Transonic Gas Dynamics. Wiley, New York (1958)
4. Chen, W., Lucente, S., Palmieri, A.: Nonexistence of global solutions for generalized Tricomi equations with combined nonlinearity. Nonlinear Anal., Real World Appl. 61(2), 103354 (2021)
5. Oguri, A., Teratani, Y., Tsutsumi, K., Sakano, R.: Current noise and Keldysh vertex function of an anderson impurity in the fermi liquid regime (2021)