1. On a backward problem for the Kirchhoff’s model of parabolic type
- Author
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Danh Hua Quoc Nam, Thi Minh Nhat Vo, and Nguyen Huy Tuan
- Subjects
Truncation method ,010103 numerical & computational mathematics ,01 natural sciences ,010101 applied mathematics ,Computational Mathematics ,Nonlinear system ,symbols.namesake ,Fourier transform ,Exact solutions in general relativity ,Computational Theory and Mathematics ,Homogeneous ,Hadamard transform ,Modeling and Simulation ,Norm (mathematics) ,symbols ,Applied mathematics ,Nonlinear boundary value problem ,0101 mathematics ,Mathematics - Abstract
We study for the first time the backward problem for nonlocal nonlinear boundary value problem of Kirchhoff’s model of parabolic type. First, we show that the problem is severely ill-posed in the sense of Hadamard. We propose two methods: the Fourier truncation method for stabilizing the problem with homogeneous source and the quasi-reversibility method for regularizing the problem with nonlinear source. Under some priori assumptions on the exact solution, we establish some stability estimates in the H 0 1 norm.
- Published
- 2019
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