Dynamical poroplasticity model with mixed boundary conditions – Theory for LMLM-type nonlinearity

We investigate the existence theory to the non-coercive fully dynamic model of poroplasticity with nonhomogeneous mixed boundary condition and constitutive equation which belongs to the class LMLM. Existence of the solution to this model is proved by using the coercive and Yosida approximations under the lowest possible assumptions about LMLM-type nonlinearity of non-gradient type. Under higher assumptions about the constitutive equation and boundary conditions (see Section 7) we obtain uniqueness and higher regularity of the solutions.