Existence of tumor invasion model with mesenchymal and epithelial transition processes in variable exponent spaces

This work illustrate the solvability of the system consist of tumor cells of two types along with epithelial cells and mesenchymal densities. The role of proteins matrix metalloproteinases and extra cellular matrix are considered. Along with the square integrability of the mesenchymal epithelial transition function, the solvability is illustrated under the Faedo–Galerkin approximation method.