Homogenization of Variational Inequalities for the p-Laplace Operator in Perforated Media Along Manifolds

We address homogenization problems of variational inequalities for the p-Laplace operator in a domain of Rn (n ? 3, p ? [2, n)) periodically perforated by balls of radius O(??) where ? > 1 and ? is the size of the period. The perforations are distributed along a (n ? 1)-dimensional manifold ? , and we impose constraints for solutions and their fluxes (associated with the p-Laplacian) on the boundary of the perforations. These constraints imply that the solution is positive and that the flux is bounded from above by a negative, nonlinear monotonic function of the solution multiplied by a parameter ? ?? , ? ? R and ? is a small parameter that we shall make to go to zero. We analyze different relations between the parameters p, n, ?, ? and ?, and obtain homogenized problems which are completely new in the literature even for the case p = 2.This work has been partially supported by the Spanish grant MINECO:MTM2013-44883-P

Phase I study of the combination of losoxantrone and cyclophosphamide in patients with refractory solid tumours

Losoxantrone is a DNA intercalator that was developed with the potential to replace anthracyclines. The recommended single agent dose of losoxantrone is 50 mg m−2 every 3 weeks. We conducted a phase I study of losoxantrone and a fixed dose of cyclophosphamide on a q3 weekly schedule. Forty-nine patients were enrolled, of which 46 were evaluable for toxicity. The dose-limiting toxicity was neutropenia at the maximum tolerable losoxantrone dose of 45 mg m−2. With granulocyte colony-stimulating factor support, significant further dose escalation of losoxantrone was achieved. Cardiotoxicity was seen with cumulative dosing. Pharmacokinetics of losoxantrone revealed linear kinetics and triphasic clearance, with significant interpatient variability. No objective responses were seen in this study. Neutropenia was dose-limiting in this combination with or without granulocyte colony-stimulating factor support. The recommended dose for further testing is cyclophosphamide 500 mg m−2 followed by losoxantrone 95 mg m−2 with granulocyte colony-stimulating factor support

Optimal control of a class of reaction-diffusion systems

The optimal control of a system of nonlinear reaction-diffusion equations is considered that covers several important equations of mathematical physics. In particular equations are covered that develop traveling wave fronts, spiral waves, scroll rings, or propagating spot solutions. Well-posedness of the system and differentiability of the control-to-state mapping are proved. Associated optimal control problems with pointwise constraints on the control and the state are discussed. The existence of optimal controls is proved under weaker assumptions than usually expected. Moreover, necessary first-order optimality conditions are derived. Several challenging numerical examples are presented that include in particular an application of pointwise state constraints where the latter prevent a moving localized spot from hitting the domain boundary.Eduardo Casas was partially supported by the Spanish Ministerio de Economía, Industria y Competitividad under Projects MTM2014-57531-P and MTM2017-83185-P. Christopher Ryll and Fredi Tröltzsch are supported by DFG in the framework of the Collaborative Research Center SFB 910, Project B6