A three-dimensional discrete model for approximating the deformation of a viral capsid subjected to lying over a flat surface in the static and time-dependent case

Abstract

In this paper, we present a three-dimensional discrete model governing the deformation of a viral capsid, modelled as a regular icosahedron and subjected not to cross a given flat rigid surface on which it initially lies in correspondence of one vertex only. First, we set up the model in the form of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable space. Second, we show the existence and uniqueness of the solution for the proposed model. Third, we numerically test this model and we observe that the outputs of the numerical experiments comply with physics. Finally, we establish the existence of solutions for the corresponding time-dependent version of the obstacle problem under consideration.

Global well-posedness for the three-dimensional generalized tropical climate model with damping

“…By virtue of Gronwall's inequality and (3), ( 5), (11) and (19), we have ∥(u, v, θ)(t)∥ 2 L 2 = 0. The proof of uniqueness of the system (1) is completed.…”

“…Combining ( 5) with (19), we get the a priori estimates. Thus we complete the proof of existence of the system (1).…”

“…Berti, Bisconti and Catania obtained a regularity criterion for 3D tropical climate model with damping thanks to which the local smooth solution (u, v, θ) can actually been extended globally in time in [1]. Moreover, we also learn from the content in [7,19,21].…”

Numerical corroboration of Koiter’s model for all the main types of linearly elastic shells in the static case

“…For what concerns the literature related to time-dependent problems in elasticity, it is worth mentioning the papers Bock and Jarusek [16,17], Bock et al [18], Piersanti [19][20][21], and Shen and Li [22]. It is also worth mentioning the papers Piersanti [23,24], Piersanti and Shen [25], Piersanti [26,27], Rodríguez-Arós [28], and Shen et al [29][30][31][32].…”

A simple approach for studying global asymptotic stability of a malware spreading model on WSNs

“…Studies on mathematical models of general types of malware will be conduced in future research. In addition, epidemiological models based on partial differential equations (PDEs) have attracted the attention of many researchers over the years (see, e.g., [4,5,9,28,31,49,52]). For this reason, studying mathematical models of malware based on PDEs is also a problem, which will be interested in.…”