No abstract

We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.

In this paper, we consider an initial boundary value problem for nonlinear Love equation with infinite memory. By combining the linearization method, the Faedo–Galerkin method, and the weak compactness method, the local existence and uniqueness of weak solution is proved. Using the potential well method, it is shown that the solution for a class of Love-equation exists globally under some conditions on the initial datum and kernel function.

We consider an extension of the concept of α , β -normal operators in single variable operator to tuples of operators, similar to those extensions of the concepts of normality to joint normality, hyponormality to joint hyponormality, and quasi-hyponormality to joint quasi-hyponormality.