On the well-posedness of a certain model with two kernels appearing in the mathematical biology

TL;DR

This paper proves the global well-posedness of a biological integro-differential model with two nonlocal kernels, using fixed point methods, contributing to the mathematical understanding of cell population dynamics.

Contribution

It establishes the well-posedness of a new integro-differential model with two kernels in biological systems, a novel result in mathematical biology.

Findings

Proves global well-posedness in a specific Sobolev space.

Uses fixed point technique for the proof.

Addresses biological relevance of the model.

Abstract

The work is devoted to establishing the global well-posedness in $W^{(1,2),2}(R\times R^{+})$ of the integro-differential problem involving the two nonlocal terms describing the diffusion and the production in the biological system in the presence of the transport term. Such model is relevant to the cell population dynamics in the Mathematical Biology. The proof is based on a fixed point technique.