| Abstract: |
| We present a nonlocal evolution system of SDEs describing marble degradation by acid particles, coupled with ODEs for the random fields evaluating the current damage at a continuum scales. The coupling particle-continuum is done via non-local operators, while the chemical reaction is assumed to be a Poisson counting process. Strong solutions to this system were found earlier and they are unique. We illustrate numerically their behavior, and finally, we point out a couple of currently open mathematical questions mostly concerning the model averaging (periodic homogenization) and reduction. |
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