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New Mathematical Trends in the Study of Materials Behavior


The aim of this collection is to provide an up-to-date view of the broad research field of nonlinear PDEs and material science with an attention to modeling, analysis and computation of fluid and solid dynamics, elasticity, complex materials and environmental phenomena. The emergence of scale structures driven by nonlinearities constitutes a major challenge to understanding continuum physics deeply founded in the PDEs framework.

We are honored to have Giuseppe Mario Coclite, Professore Ordinario di Analisi Matematica at Politecnico di Bari in Italy, and Francesco Maddalena, Associate Professor of Mathematical Analysis at Politecnico di Bari in Italy, as our esteemed guest editors for this collection. 

  1. Motivated by several applications, we investigate the well-posedness of a switched system composed by a system of linear hyperbolic balance laws and by a system of linear algebraic differential equations. This...

    Authors: Raul Borsche, Mauro Garavello and Damla Kocoglu
    Citation: Advances in Continuous and Discrete Models 2023 2023:19
  2. We prove the convergence of certain second-order numerical methods to weak solutions of the Navier–Stokes equations satisfying, in addition, the local energy inequality, and therefore suitable in the sense of ...

    Authors: Luigi C. Berselli and Stefano Spirito
    Citation: Advances in Continuous and Discrete Models 2022 2022:65
  3. Peridynamic (PD) theories have become widespread in various research areas due to the ability of modeling discontinuity formation and evolution in materials. Bond-based peridynamics (BB-PD), notwithstanding so...

    Authors: Nunzio Dimola, Alessandro Coclite, Giuseppe Fanizza and Tiziano Politi
    Citation: Advances in Continuous and Discrete Models 2022 2022:60