No abstract

We prove results on the relaxation and weak* lower semicontinuity of integral functionals of the formover the space BD(Ω) of functions of bounded deformation or over the Temam-Strang space U(Ω) := u ∈ BD(Ω) : div u ∈ L 2 (Ω) , depending on the growth and shape of the integrand f . Such functionals are interesting for example in the study of Hencky plasticity and related models.

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 LM. Existence of the solution to this model is proved by using the coercive and Yosida approximations under the lowest possible assumptions about LM-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.