One of the most crucial and lethal characteristics of solid tumors is represented by the increased ability of cancer cells to migrate and invade other organs during the so-called metastatic spread. This is allowed thanks to the production of enzymes capable of degrading the basament membrane separating the epithelial tissue from the connective one. 

I am going to consider PDEs systems describing tumor and molecules (enzymes) interaction and dynamics in a domain coupled into two distinct one, separated by a membrane. At  first I will show the derivation of membrane conditions in the limit of a zero-thickness membrane. Then, I will present an existence result on reaction-diffusion membrane problems and an application to real data.