INVERSE COEFFICIENT PROBLEM FOR THE FOURTH-ORDER BEAM EQUATION BY THE METHOD OF VARIATIONAL IMBEDDING

Jin Wen; Hong-Bo Zheng; Xin-Yi Liu; Xue-Juan Ren

doi:10.11948/20250075

2026 Volume 16 Issue 2

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Jin Wen, Hong-Bo Zheng, Xin-Yi Liu, Xue-Juan Ren. INVERSE COEFFICIENT PROBLEM FOR THE FOURTH-ORDER BEAM EQUATION BY THE METHOD OF VARIATIONAL IMBEDDING[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 724-741. doi: 10.11948/20250075

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Jin Wen, Hong-Bo Zheng, Xin-Yi Liu, Xue-Juan Ren. INVERSE COEFFICIENT PROBLEM FOR THE FOURTH-ORDER BEAM EQUATION BY THE METHOD OF VARIATIONAL IMBEDDING[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 724-741. doi: 10.11948/20250075

INVERSE COEFFICIENT PROBLEM FOR THE FOURTH-ORDER BEAM EQUATION BY THE METHOD OF VARIATIONAL IMBEDDING

1.
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2.
School of Life Sciences, East China Normal University, Shanghai 200241, China
3.
College of Information Engineering, Tarim University, No. 1487 Tarim Avenue East, Alar 843300, Xinjiang, China

Author Bio: Email: zhenghongbo020416@163.com(H.-B. Zheng); Email: liuxinyi20020425@163.com(X.-Y. Liu); Email: renxuejuan1010@163.com(X.-J. Ren)
Corresponding author: Email: wenjin0421@163.com(J. Wen)

Abstract

Abstract

This paper presents an inverse problem related to a fourth-order beam equation, where the coefficient at the zeroth-order term is unknown. Based on the simple approximation lemma, we employ a technique known as the method of variational imbedding to establish the existence and uniqueness of a weak solution for a variational problem. Finally, we provide several numerical examples using the finite difference method to demonstrate the efficiency and accuracy of our proposed approach.
- Inverse coefficient /
- fourth-order beam equation /
- variational imbedding /
- finite difference
MSC: 35R25, 65M30

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References

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