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I'm trying to study a research paper of lava flows, I require some help with solving these type of pde's . I'm well aware of finite volume and difference methods along with numerical techniques for solving pde's

May someone help me with the initial steps which I must do in order to solve this problem.

I am attaching the equations which are needed to be solved. The eq3 is the governing equation, rest all describe the co-efficient's temperature dependence and their variations.

This is the paper I'm referring to :

https://link.springer.com/article/10.1007/BF01081978 https://link.springer.com/content/pdf/10.1007%2FBF01081978.pdf

The equations are attached in this image file.

Problem formulation

Please let me know, if anything is not clear. Thanks

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