Decay for the solutions of nonlinear abstract damped evolution equations with applications to partial and ordinary differential systems
The paper is devoted to the investigation of general abstract evolution equations \([P(u'(t))]'+A(u(t)) + Q(t,u(t),u'(t)) + F(u(t))=0\), where \(A,F,P\) and \(Q\) are nonlinear operators in appropriate Banach spaces, and \(t>0\) is the time variable. Equations of the above form are described according to the asymptotic behavior of solutions. Assuming that a global solution exists, the authors derive precise decay estimates for the energy functional \(E(t)\) in each case. It is shown that the results can be applied for instance to quasilinear hyperbolic equations with nonlinear damping.
scientific article; zbMATH DE number 1453630