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On A Class Of Multiscale Cancer Cell Migration Models: Well-posedness In Less Regular Function Spaces

Thomas Lorenz, Christina Surulescu

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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.