A nonlinear model for marble sulphation including surface rugosity: theoretical and numerical results

TL;DR

This paper introduces a nonlinear model for marble sulphation that incorporates surface rugosity, providing theoretical proofs of well-posedness and numerical simulations to illustrate the model's behavior.

Contribution

The paper develops a new nonlinear model for marble sulphation including surface rugosity and proves existence and uniqueness of solutions.

Findings

Model captures effects of surface rugosity on sulphation

Proves local and global well-posedness of the model

Numerical simulations demonstrate key features of the model

Abstract

We consider an evolution system describing the phenomenon of marble sulphation of a monument, accounting of the surface rugosity. We first prove a local in time well posedness result. Then, stronger assumptions on the data allow us to establish the existence of a global in time solution. Finally, we perform some numerical simulations that illustrate the main feature of the proposed model.