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- 2017
一类退化抛物型方程反问题的收敛性分析
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Abstract:
摘要： 考虑了一类利用附加观测数据重构二阶非散度退化抛物型方程的主项系数的反问题,该问题被转化为一个最优控制问题。本文的问题在于主项系数是未知的,而方程的退化程度通常是由主项系数的性质所决定的。通过引入赋权的Sobolev空间和一些新的源条件,并对主项系数的允许函数类附加了较强的正则性条件,证明了最优解的收敛性。
Abstract: This paper consider an inverse problem of reconstructing the principal coefficient in a second order degenerate parabolic equation of non-divergence form by using some additional observation data. It is transformed into an optimal control problem. The major problem is that the principal coefficient is unknown, but the degenerate degree of equation is determined, in general, by the principal coefficient. By introducing some weighted Sobolev spaces and some new source conditions, and adding a strong regularity condition to the admissible function set of the principal term, we prove the convergence of the optimal solution
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