Existence, Regularity And Asymptotic Behavior Of Solutions For Abstract Strongly Damped Wave Equations

Based on the theory of semigroups ,the paper studies the existence ,uniqueness , regularity and asymptotic behavior of solutions to the initial value problems for semilinear strongly damped wave equationsin Banach spaces and the mains results are as follows:1.The existence and uniqueness of saturated mild solutions and global mild solutions to the initial value problems for semilinear strongly damped wave equations are discusses by using analytic semigroups theory and Banach fixed point theorem in Banach spaces.2.By using analytic semigroups theory, We discuss the regularity of solutions to the initial value problems for linear abstract strongly damped wave equations .On the other hand , We discuss the regularity of saturated mild solutions and obtained existence of solutions classical saturated solutions and global classical solutions to the initial value problems for semilinear strongly damped wave equations.3.Under analytic semigroups is exponentially stable , We discuss asymptotic behavior of global mild solutions to the initial value problems for linear abstract strongly damped wave equations and semilinear strongly damped wave equations by using analytic semigroups theory .Finally, The existence ,uniqueness , regularity and asymptotic behavior of solutions and obtained by apply the abstract results to discuss concrete initial boundary value problems for strongly damped wave equations.