Geodesic
Application of Rothe's method to a parabolic inverse problem with nonlocal boundary condition
Applications of Mathematics, Tome 67 (2022) no. 5, pp. 573-592.

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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 $u_0\in H^1(\Omega )$ is presented by means of the Rothe time-discretization method. Further approximation scheme via Rothe's method is constructed for the problem when $u_0\in L^2(\Omega )$ and the integral kernel in the nonlocal boundary condition is symmetric.
DOI : 10.21136/AM.2021.0029-21
Classification : 35K58, 35R30, 65M20
Keywords: Rothe's method; nonlocal boundary condition; semilinear parabolic equation; inverse source problem 
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Jo, Yong-Hyok; Ri, Myong-Hwan. Application of Rothe's method to a parabolic inverse problem with nonlocal boundary condition. Applications of Mathematics, Tome 67 (2022) no. 5, pp. 573-592. doi : 10.21136/AM.2021.0029-21. http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0029-21/

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