On a class of multiscale cancer cell migration models: Well-posedness in less regular function spaces

The system of functional differential equations considered here is motivated by a concrete class of multiscale models for tumor cell migration involving chemotaxis, haptotaxis, and subcellular dynamics proposed in [J. Kelkel and C. Surulescu, A multiscale approach to cell migration in tissue networks, Math. Models Methods Appl. Sci. 22 (2012) 1150017]. Tissue fibers, cell densities and concentrations of chemotactic signals are assumed to be just square Lebesgue integrable in space, but not necessarily essentially bounded (as in [J. Kelkel and C. Surulescu, A multiscale approach to cell migration in tissue networks, Math. Models Methods Appl. Sci. 22 (2012) 1150017] and related previous settings). The focus of interest is on sufficient conditions for the well-posedness of the underlying larger problem class.