Quasilinear equations that are not solved for the higher-order time derivative
The author discusses the solvablity of a higher order quasilinear differential equation with a degenerate operator at the derivative part. By the projection method, some existence and uniqueness theorems are proved for linear equation under initial boundary condition, and then extended to nonlinear equation under the assumption that the nonlinearity is locally Lipschitz. The obtained results are applied to the motion equation of the Kelvin-Voigt fluid.
scientific article; zbMATH DE number 6501749
scientific article