The Cauchy problem for Boussinesq equations with general elliptic part

Abstract

In this paper, the existence and uniqueness of solution of the Cauchy problem for abstract Boussinesq equation is obtained. The leading part of the equation include general elliptic operator and abstract positive operator in a Banach space E. Since the Banach space E and linear operators are sufficiently large classes, by choosing their we obtain the existence and uniqueness of solution of numerous classes of generalized Boussinesq type equations which occur in a wide variety of physical systems. By applying this result, the Wentzell-Robin type mixed problem for Boussinesq equations and the Cauchy problem for finite or infinite systems of Boussinesq equations are studied.