Nonsmooth analysis of doubly nonlinear evolution equations

In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general sufficient conditions, on the dissipation potential and the energy functional,for existence of solutions to the related Cauchy problem. We prove our main existence result by passing to the limit in a time-discretization scheme with variational techniques. Finally, we discuss an application to a material model in finite-strain elasticity.Comment: 45 page

Quasistatic delamination of sandwich-like Kirchhoff-Love plates

A quasistatic rate-independent adhesive delamination problem of laminated plates with a finite thickness is considered. By letting the thickness of the plates go to zero, a rate-independent delamination model for a laminated Kirchhoff-Love plate is obtained as limit of these quasistatic processes. The same dimension reduction procedure is eventually applied to processes which are sensitive to delamination modes, namely opening vs. shearing is distinguishe

Measuring systemic risk with a dynamic copula-based approach

This study examines the extent of systemic risk embedded in the credit and equity markets using a conditional value-at-risk (CoVaR) measure. We implement a copula-based CoVaR approach with different perspectives of a dependence structure based on a generalized autoregressive score model. In parallel, we select the credit default swap spread and stock price data of five companies in the financial sector ??? American Express, BBVA, Goldman Sachs, Morgan Stanley, and Wells Fargo ??? from 2001 to 2013, and include data on the global financial crisis of 2007???2008. We then divide the data into three time periods: pre-crisis, during the crisis, and post-crisis. We conduct time-varying marginal modelling, and copula parameter estimation, and then compute CoVaR values with the best-fit copula model. Comparative empirical tests provide financial implications for systemic risk management

From Visco-Energetic to Energetic and Balanced Viscosity Solutions of Rate-Independent Systems

This paper focuses on weak solvability concepts for rate-independent systems in a metric setting. Visco-Energetic solutions have been recently obtained by passing to the time-continuous limit in a time-incremental scheme, akin to that for Energetic solutions, but perturbed by a `viscous' correction term, as in the case of Balanced Viscosity solutions. However, for Visco-Energetic solutions this viscous correction is tuned by a fixed parameter $\mu$. The resulting solution notion is characterized by a stability condition and an energy balance analogous to those for Energetic solutions, but, in addition, it provides a fine description of the system behavior at jumps as Balanced Viscosity solutions do. Visco-Energetic evolution can be thus thought as `in-between' Energetic and Balanced Viscosity evolution. Here we aim to formalize this intermediate character of Visco-Energetic solutions by studying their singular limits as $\mu\downarrow 0$ and $\mu\uparrow \infty$. We shall prove convergence to Energetic solutions in the former case, and to Balanced Viscosity solutions in the latter situation