Blow-up of Solutions and Local Solvability of an Abstract Cauchy Problem of Second Order with a Noncoercive Source - Artem’eva, M. V.; Korpusov, M. O. (Computational mathematics and mathematical physics, 2023)
An abstract Cauchy problem for a second-order differential equation with nonlinear operator coefficients is considered. The local solvability of the problem in suitable spaces of abstract continuous and differentiable functions is proved. Sufficient conditions for finite-time blow-up of its solutions are obtained.