As is known, the Blaschke tensor A (a symmetric covariant 2-tensor) is one of the fundamental Möbius invariants in the Möbius differential geometry of submanifolds in the unit sphere S n , and the eigenvalues of A are referred to as the Blaschke eigenvalues. In this paper, we shall prove a classification theorem for immersed umbilic-free submanifolds in S n with a parallel Blaschke tensor. For proving this classification, some new kinds of examples are first defined.
We consider a type of fuzzy viscoelastic integro-differential model in this paper. With the aid of some appropriate hypotheses, a unified method and the multiplier technique are implemented to get priori estimates precisely without constructing any auxiliary function. By establishing the estimation of energy function, we derive the stability result of the global solution, and we calculate the estimations of energy attenuation in exponential and polynomial forms, respectively.
This paper considers the fuzzy viscoelastic model with a nonlinear source u t t + L u + ∫ 0 t g t − ζ Δ u ζ d ζ − u γ u − η Δ u t = 0 in a bounded field Ω. Under weak assumptions of the function g t , with the aid of Mathematica software, the computational technique is used to construct the auxiliary functionals and precise priori estimates. As time goes to infinity, we prove that the solution is global and energy decays to zero in two different ways: the exponential form and the polynomial form.
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