On the well-posedness of some model with the cubed Laplacian arising in the Mathematical Biology

In the article we establish the global well-posedness in W^{1,(6,2)}(R \times R+) of the integro-differential equation containing the cube of the one dimensional Laplacian and the transport term. Our proof relies on a fixed point technique. Furthermore, we formulate the condition leading to the existence of the nontrivial solution for our problem under the consideration. This problem is relevant to the cell population dynamics in the Mathematical Biology.