This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.

Recent trends and views on elliptic quasi-variational inequalities.- The incompatibility operator: from Riemann intrinsic view of Geometry to a new model of elasto-plasticity.- Nonlocal phase field models of viscous Cahn-Hilliard type.- Invariant and quasi-invariant measures for equations in Hydrodynamics.- Long-range phase coexistence models: recent progress on the fractional Allen-Cahn equation.- Construction of Non-asymptotic Confidence Sets in 2-Wasserstein Space.- On the use of ADMM for image inverse problems: the pros and the cons of matrix inversions.- Models and numerical methods for electrolyte flows.- Consequences of uncertain friction for the transport of natural gas through passive networks of pipelines.- Probabilistic methods for spatial multihop communication systems.- Mathematical modeling of semiconductors: from quantum mechanics to devices.- Gradient structures for flows of concentrated suspensions.- Variational and quasi-variational inequalities with gradient type constraints.- Models of dynamic damage and phase-field fracture, and their various time discretisations.