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We prove the null controllability of the relaxed Stefan problem, which models phase transitions in two-phase systems. The technique relies on the penalty approximation of the differential inclusion describing the phase dynamics, solving a constrained minimization problem, and passing to the limit.

We propose to model the mammalian lungs as a viscoelastic deformable porous medium with a hysteretic pressure–volume relationship described by the Preisach operator. Breathing is represented as an isothermal time-periodic process with the gas exchange between the interior and exterior of the body. The main result consists of proving the existence of a periodic solution under an arbitrary periodic forcing in suitable function spaces.

Classification of inner processes during loading and unloading tests in models of hypoplasticity developed by D. Kolymbas for the constitutive behavior of granular materials is the main aim of this work. We focus on a modified model proposed by Bauer. By introducing a dimensionless time parameter s, we transform the constitutive equation into a rate-independent form, and study the stress paths in different proportional loading regimes.

The article deals with the technical literacy and implementation of the Industry 4.0 at elementary schools. It deals with the importance of construction kit in development of children’s technical thinking. The article presents the results of research taken at elementary schools in the Hradec Kralove Region. The research is dealing with the problematic of teaching the subject “Polytechnic creation” and is dealing with the use of construction kits during that subject.

The diffusion equation with a bounded saturation range under the time derivative and with Robin boundary conditions is shown to admit a regular bounded solution provided that the saturation function and the permeability coefficient have controlled decay at infinity. The result remains valid even if Preisach hysteresis is present in the pressure-saturation relation. The method of proof is based on a Moser-Alikakos iteration scheme which is compatible with a generalized Preisach energy dissipation mechanism.