一类确定伪抛物型方程常数系数的反问题

A Class of Inverse Problems to Determine the Constant Coefficient for the Pseudoparabolic Equation

文章讨论了一类具有特殊初值条件的伪抛物型方程确定常数系数的反问题。首先,在假定常数系数已知的条件下,利用Fourier变换方法给出了方程的形式解;然后,再利用附加条件导出未知系数满足的关系式;最后,给出了此类反问题解的存在唯一性结论。

This paper deals with a class of inverse problems to determine the constant coefficient for the pseudoparabolic equation with special initial condition. Firstly, it is assumed that the constant coefficient is known, and by Fourier transform we work out the general representation of the pseudoparabolic equation given. Then the relationship which unknown coefficient satisfies from additional condition is derived.Finally we deduce the existence and uniqueness of solution of the pseudoparabolic equation.