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Consider the operator generated by problem (5.1).
Let denote the operator in generated by problem (7.1).
Let Q denote the operator generated by problem (5.1 - 5.2 5.1 - 5.2
Let Q denote the operator, generated by problem (4.4) and (5.1).
Moreover, we prove that the operator generated by problem (1.1) is positive.
Let be a differential operator generated by problem (3.1 - 3.2 3.1 - 3.2hat is, (3.6).
Let denote the operator generated by problem (3.11) for ; that is, (4.30).
Zheng and Milani [2] proved that the dynamical systems generated by problem (1.1)–(1.3) admit exponential attractors and inertial manifolds.
At the same time, (L q, alpha, beta)) denotes the self-adjoint operator generated by problem (1.1 - 1.3 1.1 - 1.3g., [1–3]).
Consider the differential operator Q ε generated by problem (1.5), i.e., From Theorem 3.1 we obtain the following.
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