Abstract

Existence and uniqueness theorems for solutions of inverse problems of determining the time-dependent absorption coefficient in a degenerate parabolic equation with two independent variables are proved. An integral observation condition is additionally imposed. The unknown absorption coefficient is sought in the class of bounded functions on \([0,T]\). Examples of the inverse problems are given for which the conditions of the theorems proved in the work are satisfied.

中文翻译：

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确定L∞类退化抛物方程的吸收系数的反问题

摘要

证明了具有两个自变量的退化抛物方程中确定时间相关吸收系数的反问题的解的存在唯一性定理。附加地施加了积分观察条件。在\（[0，T] \）上的有界函数类中寻找未知吸收系数。给出了反问题的例子，这些反问题的例子满足了工作中证明的定理条件。