Understanding how climate change might influence the distribution and abundance of crop pests is fundamental for the development and the implementation of pest management strategies. Here we present and apply a modelling framework assessing the non-linear physiological responses of the life-history strategies of the Mediterranean fruit fly (Ceratitis capitata, Wiedemann) to temperature. The model is used to explore how climate change might influence the distribution and abundance of this pest in Europe. We estimated the change in the distribution, abundance and activity of this species under current (year 2020) and future (years 2030 and 2050) climatic scenarios. The effects of climate change on the distribution, abundance and activity of C. capitata are heterogeneous both in time and in space. A northward expansion of the species, an increase in the altitudinal limit marking the presence of the species, and an overall increase in population abundance is expected in areas that might become more suitable under a changing climate. On the contrary, stable or reduced population abundances can be expected in areas where climate change leads to equally suitable or less suitable conditions. This heterogeneity reflects the contribution of both spatial variability in the predicted climatic patterns and non-linearity in the responses of the species’ life-history strategies to temperature.

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We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.

We prove existence and regularity for the solutions to a Cahn-Hilliard system describing the phenomenon of phase separation for a material contained in a bounded and regular domain. Since the first equation of the system is perturbed by the presence of an additional maximal monotone operator, we show our results using suitable regularization of the nonlinearities of the problem and performing some a priori estimates which allow us to pass to the limit thanks to compactness and monotonicity arguments. Next, under further assumptions, we deduce a continuous dependence estimate whence the uniqueness property is also achieved. Then, we consider the related sliding mode control (SMC) problem and show that the chosen SMC law forces a suitable linear combination of the temperature and the phase to reach a given (spacedependent) value within finite time.

Abstract. We consider a quasilinear elliptic equation, with right hand side measure, which does not satisfy the usual coercivity assumption. We prove an existence result in the line of the Fredholm alternative. For this purpose we develop a variant of degree theory suited to this setting.