### Korotkii A.I. Ismail-Zadekh A.T. Kovtunov D.A. Melnik O.E. Tsepelev I.A.

## Determination of volcanic lava properties based on measurements of some physical parameters on its surface

### Reporter: Korotkii A.I.

We consider a problem of volcanic lava flow to determine the lava thermodynamic parameters from some measurement on the surface of the lava. Mathematically this problem is reduced to an inverse boundary problem for viscous incompressible heterogeneous heat-conducting fluid flow. Using the information on a part of the model boundary (e.g. temperature and heat flow measured at the surface) we determine the missing conditions at the remaining part of the boundary and then solve the problem to reconstruct the physical parameters of fluid in the model domain. This problem can be referred to as a problem of extension of the solution from a part of the boundary to the entire domain. This problem is ill-posed. We have developed the method and the solution algorithms for the problem and considered the case of steady-state flow. Assuming that the temperature and the heat flow are prescribed (let us say, measured) at the upper surface of the model domain, we determine the flow characteristics in the entire model domain. Using a Tikhonov-type method we have performed computations of model examples and showed that in the case of smooth input data the lava temperature and flow can be reconstructed with a high precision. We shall present and discuss the results of the numerical experiments. The work is supported by the Russian Science Foundation (Project No. 14-17-00520).

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