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

Elena Bonetti; Cecilia Cavaterra; Francesco Freddi; Maurizio Grasselli; Roberto Natalini

doi:10.3934/cpaa.2019048

Article Contents

2019, Volume 18, Issue 2: 977-998. Doi: 10.3934/cpaa.2019048

This issue Previous Article Fractal analysis of canard cycles with two breaking parameters and applications Next Article

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

1.
Dipartimento di Matematica "F. Enriques", Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy
2.
Istituto di Matematica Applicata e Tecnologie Informatiche "Enrico Magenes", CNR, Via Ferrata 1, 27100 Pavia, Italy
3.
Dipartimento di Ingegneria e Architettura, Università degli Studi di Parma, Parco Area delle Scienze 181/A, 43124 Parma, Italy
4.
Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi 9, 20133 Milano, Italy
5.
Istituto per le Applicazioni del Calcolo "M. Picone", CNR, Via dei Taurini 19, 00185 Roma, Italy

* Corresponding author
* Corresponding author

Received: February 2018

Revised: June 2018

Published: October 2018

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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.

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Mathematics Subject Classification: Primary: 35M33; Secondary: 65M60, 74N25.

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Figure 1. Evolution of $c$ along the left vertical bounder for $r$ piecewise and $\nu (r)$ a) linear and b) parabolic

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Figure 2. Evolution of $s$ along the left vertical bounder for $r$ piecewise and $\nu (r)$ a) linear and b) parabolic

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Figure 3. Evolution of $r$ along the left vertical bounder for $r$ piecewise and $\nu (r)$ a) linear and b) parabolic

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Figure 4. Evolution of $c$ along a horizontal line within the solid located at a) $x_2 = 0.25$ and b) $x_2 = 0.75$ assuming parabolic relationship for $\nu (r)$

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Figure 5. Evolution of $s$ along a horizontal line within the solid located at a) $x_2 = 0.25$ and b) $x_2 = 0.75$ assuming parabolic relationship for $\nu (r)$

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Figure 6. Concentration of $SO_2$ within the solid at different time step a) $n = 5$ and b) $n = 15$ assuming parabolic relationship for $\nu (r)$

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Figure 9. Evolution of $r$ along the left vertical bounder for $r$ random and $\nu (r)$ a) linear and b) parabolic

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Figure 7. Evolution of $c$ along the left vertical bounder for $r$ random and $\nu (r)$ a) linear and b) parabolic

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Figure 8. Evolution of $s$ along the left vertical bounder for $r$ random and $\nu (r)$ a) linear and b) parabolic

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