Double nonlinear diffusion equations in a two-component domain

Abstract A system of two double nonlinear diffusion equations acting on two different rectangles in $${\mathbb {R}}^2,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> connected by the nonlinear boundary conditions on the contact line, is studied. We prove the existence and uniqueness of a weak solution. Moreover, we illustrate the solution using numerical scheme based on finite volume discretization in space and explicit time discretization. The paper is an extension of previous results of Filo and Pluschke, who dealt with a system of two porous medium equations defined on two different components of the real line connected by a nonlinear contact condition.