Дослiджуються оберненi задачi для параболiчного рiвняння з виродженням, молодший коефiцiєнт якого є лiнiйним многочленом за просторовою змiнною з двома невiдомими залежними вiд часу функцiями. Виродження рiвняння спричинено монотонно зростаючою функцiєю вiд часу, яка розмiщена в ньому при похiднiй за часом. Встановлено умови iснування та єдиностi класичних розв’язкiв згаданих задач у випадку слабкого виродження.

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