On the well-posedness of some model with the cubed Laplacian arising in the Mathematical Biology
Messoud Efendiev, Vitali Vougalter
TL;DR
The global well-posedness of the integro-differential equation containing the cube of the one dimensional Laplacian and the transport term of the integro-differential equation containing the cube of the one dimensional Laplacian is established.
Abstract
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.