Help with solving coupled non-linear diffusion equations

I am studying the dynamics of thin liquid films. In this context, I obtained the following set of equations:
where y=y(x,t), r=r(x,t) are unknown functions which their solution I am looking for (and all other coefficients are constants). How can I solve these equations using matlab (preferably by utilizing it's in-house code)?

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2017-7-11

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2017-7-11

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