Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.

The engagement of yugoslav technical cooperation experts in post-colonial Algeria (1962-1990). A global microhistory of east-south relations

The venture of socialist Eastern Europe in assisting the development efforts of the post-colonial countries opened up official migratory channels to the Global South for a specific labour group engaged under international technical cooperation programmes. By taking post-colonial Algeria as a space of East-South interactions and intense inter-socialist competition, the thesis studies labour mobility from socialist Yugoslavia of a heterogeneous group labelled “technical cooperation experts” in the period from 1962 to 1990. While CMEA members dispatched to the country personnel in great numbers, after 1965, Yugoslavia failed to do so. Tracing them beyond the institutional level, the thesis aims at detecting and exposing factors which inhibited the attempts to increase the presence of Yugoslav technical experts in Algeria. It argues that instead of building an alternative, solidarity-based aid model, Yugoslav technical cooperation with the developing countries was reduced to mediation in the employment of highly-skilled labour abroad. The cooperation scheme, which differed from one of its Eastern European counterparts, manifested in the employment and legal status as well as everyday life and work experiences of Yugoslav citizens. Relying on the methodological approach of global microhistory, which strongly favours the micro-historical analysis of primary sources in studying global processes, the thesis provides a more comprehensive and nuanced understanding of Yugoslav globalization endeavours. By shifting the focus to the experiences of ordinary people who were under the strong influence of globalization forces of the Cold War era, the thesis adds a “human” dimension to the history of East-South relations.