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New Mathematical Trends in the Study of Materials Behavior

Scope:

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. 



  3. 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
    Content type: Research Published on:

  4. We introduce and study a variational model for signal and image analysis based on Riemann–Liouville fractional derivatives. Both the one-dimensional and two-dimensional cases are studied. The model exploits a ...

    Authors: Antonio Leaci and Franco Tomarelli
    Citation: Advances in Continuous and Discrete Models 2023 2023:14
    Content type: Research Published on:

  6. Peridynamics is a nonlocal generalization of continuum mechanics theory which addresses discontinuous problems without using partial derivatives and replacing them by an integral operator. As a consequence, it...

    Authors: Luciano Lopez and Sabrina Francesca Pellegrino
    Citation: Advances in Continuous and Discrete Models 2022 2022:70
    Content type: Research Published on:

  7. 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
    Content type: Research Published on:

  8. 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
    Content type: Review Published on: