On the well-posedness of a certain model with the bi-Laplacian appearing in the Mathematical Biology

TL;DR

The work is devoted to the global well-posedness of the integro-differential problem involving the square of the one dimensional Laplace operator along with the drift term of the integro-differential problem involving the square of the one dimensional Laplace operator.

Abstract

The work is devoted to the global well-posedness in W^{1, (4, 2)}(R\times R^{+}) of the integro-differential problem involving the square of the one dimensional Laplace operator along with the drift term. Our proof is based on a fixed point technique. Moreover, we provide the assumption leading to the existence of the nontrivial solution for the problem under the consideration. Such equation is relevant to the cell population dynamics in the Mathematical Biology.