Linearized stability for hyperbolic evolution equations with semilinear boundary conditions
The author presents an abstract setting for semilinear hyperbolic equations with nonlinear boundary conditions. Then a criterion for the (uniform, exponential) stability of equilibria is provided in terms of the growth bound of the semigroup generated by a suitably defined linearized operator. Under slightly stronger assumptions, a sufficient condition is given which only involves spectral properties of the linearized operator.
semilinear hyperbolic equations with nonlinear boundary conditions
scientific article; zbMATH DE number 4119035