【摘要】 研究了一类基于积分观测条件重构二阶非散度抛物型方程的辐射系数的反问题,这里的辐射系数仅依赖于空间变量.首先利用Cauchy不等式与Gronwall不等式得到正问题解的先验估计式;然后将原问题转化为非线性算子方程,基于Schauder不动点定理,证明了反问题解的存在性;最后基于正问题解的一些先验估计式和附加条件,得到了反问题解唯一的充分条件.更多还原

【Abstract】 This paper investigates an inverse problem of using integral observation condition to reconstruct the radiative coefficient in second order nondivergence parabolic equations,and the radiative coefficient is only space dependent.Firstly,a-priori estimates of the direct problem are obtained by using Cauchy inequality and Gronwall inequality.Secondly,the original problem is transformed into a non-linear operator equation, and the existence is proved based on Schauder fixed point theorem.Finally,based on some a-priori estimates of the direct problem and additional conditions,a sufficient condition for the uniqueness of the solution is obtained.更多还原