Rothe方法在非局部边界条件抛物型反问题中的应用

Pub Date : 2021-10-19 DOI:10.21136/AM.2021.0029-21

Yong-Hyok Jo, Myong-Hwan Ri

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引用次数: 0

摘要

我们考虑了具有非局部边界条件的半线性抛物型方程中确定纯时变源的一个反问题。利用Rothe时间离散化方法，给出了初值为u0∈H1（Ω）的问题的解的近似格式和适定性。对于u0∈L2（Ω）且非局部边界条件下的积分核是对称的问题，利用Rothe方法构造了进一步的逼近格式。

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

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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