Sufficient conditions on the forcing terms for the global solvability of dissipative Kirchhoff equations
This paper concerns global unique solvability of abstract hyperbolic equations of the type \[ \partial^2_tu+m(\| A^{1/2}u\|^2)+\gamma\partial_tu=f(t), \] where \(A\) is a nonnegative self-adjoint operator. There are given a sufficient condition on the forcing \(f\) for global existence and a necessary condition for the existence of bounded solutions.
scientific article; zbMATH DE number 1836624