ILL-POSEDNESS

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Fractional Tikhonov Regularization Method for a Time-Fractional Backward Heat Equation with a Fractional Laplacian被引量：1
《Journal of Partial Differential Equations》2018年第4期333-342,共10页WANG Jianlin XIONG Xiangtuan CAO Xiaoxiao 
the Natural Science Foundation of Northwest Normal University,China(No NWNU-LKQN-17-5).
In this paper,we consider a time-fractional backward problem with a fractional Laplacian.We propose a fractional Tikhonov regularization method for solving this problem under the the a-priori parameter choice rule.Err...
关键词：INVERSE problem ILL-POSEDNESS ERROR ESTIMATE FRACTIONAL REGULARIZATION method 
Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space
《Journal of Partial Differential Equations》2015年第4期315-331,共17页LI Jinmei XIONG Xiangtuan 
The authors would like to thank the reviewers for their very careful reading and for pointing out several mistakes as well as for their useful comments and suggestions. The research was partially supported by a grant from the Key （Keygrant） Project of Chinese Ministry of Education （No 212179） and Natural Science Foundation of Gansu Province （No 145RJZA037）.
In this paper we consider a semi-descretization difference scheme for solving a Cauchy problem of heat equation in two-dimensional setting. Some error estimates are proved for the semi-descretization difference regula...
关键词：2D inverse heat conduction problem ILL-POSEDNESS REGULARIZATION error estimate finite difference 
Well- and Ill-Posedness Issues for a Class of 2D Wave Equation with Exponential Growth
《Journal of Partial Differential Equations》2011年第4期361-384,共24页MAHOUACHI Olfa SAANOUNI Tarek 
Extending the previous work [1], we establish well-posedness results for a more general class of semilinear wave equations with exponential growth. First, we investigate the well-posedness in the energy space. Then, w...
关键词：Nonlinear wave equation WELL-POSEDNESS ILL-POSEDNESS Moser-Trudinger inequality finite speed of propagation. 
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