Multi-Parameter Inverse Problems of the Nonlinear Phase Field Model

TIAN Yu; YANG Liu; YI Haihong

doi:10.21656/1000-0887.450160

Volume 46 Issue 10

Oct. 2025

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TIAN Yu, YANG Liu, YI Haihong. Multi-Parameter Inverse Problems of the Nonlinear Phase Field Model[J]. Applied Mathematics and Mechanics, 2025, 46(10): 1354-1366. doi: 10.21656/1000-0887.450160

Citation:

TIAN Yu, YANG Liu, YI Haihong. Multi-Parameter Inverse Problems of the Nonlinear Phase Field Model[J]. Applied Mathematics and Mechanics, 2025, 46(10): 1354-1366. doi: 10.21656/1000-0887.450160

Citation:

TIAN Yu, YANG Liu, YI Haihong. Multi-Parameter Inverse Problems of the Nonlinear Phase Field Model[J]. Applied Mathematics and Mechanics, 2025, 46(10): 1354-1366. doi: 10.21656/1000-0887.450160

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Multi-Parameter Inverse Problems of the Nonlinear Phase Field Model

doi: 10.21656/1000-0887.450160

School of Mathematics and Science, Lanzhou Jiaotong University, Lanzhou 730070, P.R.China

Funds:

The National Science Foundation of China(61663018；11961042)

Received Date: 2024-05-30
Rev Recd Date: 2024-06-27

Available Online: 2025-11-13

Abstract

Abstract

The inverse problem of simultaneously inverting 2 time-independent coefficients in the nonlinear phase-field model was investigated with given terminal measurement data. Unlike the usual parabolic equations, a nonlinear parabolic system of equations was studied. Based on the optimal control framework, the inverse problem was transformed into an optimization problem. The existence and necessary condition of the minimizer for the cost functional were established. The uniqueness and stability of the minimizer were deduced from the necessary condition.
- inverse problem,
- nonlinear phase-field model,
- optimal control,
- existence,
- stability,
- uniqueness

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References(17)

References

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