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Application of Rothe’s Method to a Parabolic Inverse Problem with Nonlocal Boundary Condition

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Abstract

We consider an inverse problem for the determination of a purely time-dependent source in a semilinear parabolic equation with a nonlocal boundary condition. An approximation scheme for the solution together with the well-posedness of the problem with the initial value u0 ∈ H1(Ω) is presented by means of the Rothe time-discretization method. Further approximation scheme via Rothe’s method is constructed for the problem when u0 ∈ L2(Ω) and the integral kernel in the nonlocal boundary condition is symmetric.

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Acknowledgments

We are very grateful to the referee for carefully reading this paper and for his/her helpful comments. Many thanks also go to Professor Yong-Ho Kim for his valuable suggestions.

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Authors and Affiliations

  1. Department of Applied Mathematics, Kim Chaek University of Technology, Pyongyang, Democratic People’s Republic of Korea

    Yong-Hyok Jo

  2. Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People’s Republic of Korea

    Myong-Hwan Ri

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  1. Yong-Hyok Jo
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  2. Myong-Hwan Ri
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Correspondence to Yong-Hyok Jo.

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Jo, YH., Ri, MH. Application of Rothe’s Method to a Parabolic Inverse Problem with Nonlocal Boundary Condition. Appl Math 67, 573–592 (2022). https://doi.org/10.21136/AM.2021.0029-21

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  • DOI: https://doi.org/10.21136/AM.2021.0029-21

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