We prove the uniqueness of weak solutions of initial boundary value problemsEach functionaiis required to be sufficiently smooth and must satisfy the following conditions:$$e) sumlimits_1^n {ij} partial _{eta _j eta _h }^2 a_i (x, ldots , eta 1, ldots , eta _n )xi _i xi _j leqslant 0, h = 1, ldots , n,$$for some positive constantsK0, α, some non negative constantsKi, some positive functionsH(t)∈L1(0,T) and for all ξ≡(ξi), η
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