Well-posedness and exponential equilibration of a volume-surface reaction-diffusion system with nonlinear boundary coupling

We consider a model system consisting of two reaction-diffusion equations, where one species diffuses in a volume while the other species diffuses on the surface which surrounds the volume. The two equations are coupled via a nonlinear reversible Robin-type boundary condition for the volume species and a matching reversible source term for the boundary species. As a consequence of the coupling, the total mass of the two species is conserved. The considered system is motivated for instance by models for asymmetric stem cell division. Firstly we prove the existence of a unique weak solution via an iterative method of converging upper and lower solutions to overcome the difficulties of the nonlinear boundary terms. Secondly, our main result shows explicit exponential convergence to equilibrium via an entropy method after deriving a suitable entropy entropy-dissipation estimate for the considered nonlinear volume-surface reaction-diffusion system.Comment: 31 page

Polish spatial expressions in early L2 development: The impact of form-based input enhancement

This preliminary study investigates the impact of focus-on-form input enhancement on the oral production of Polish spatial expressions by novice L2 learners. Two groups of French learners were exposed to the communicative input which differed on whether or not their attention was drawn to specific morphosyntactic properties of the target language: Form-based input vs. Meaning-based input. After 14 hoursof exposure to the TL input, the learners took a verbal route direction-giving task. The inter-group results reveal a support-ive effect of the form-based instructionon the processing and learning of target constructions. The intra-learner results imply the important role of individuality. Final findings suggest complex and multifactorial input-learner interdependence

The legal status of an intercompany trade union following amendments to the trade union act : selected issues

This article is devoted to the inter-company trade union organization after the amendment to the Trade Union Act. The inter-company trade union organization is relatively rarely subject of studies in labour law. Usually it is considered that the arrangements made for the company trade union organizations relate also to intercompany trade union organisation. Meanwhile, a more detailed analysis shows that the inter-company trade union organization is characterized by far-reaching specificity, and its regulation based largely on references to regulations governing the legal status of the company trade union organization is not always adequate. This generates numerous practical problems. In this text, the author analyzes several particularly important issues regarding intercompany trade union organization in connection with the amendment to the Trade Union Act, which entered into force on January 1, 2019