Ho Thi Kim Van. On a Kirchhoff’s Model for Nonclassical Diffusion Equation. Dynamic Systems and Applications 30 (2021) No.3, 347-357

https://doi.org/10.46719/dsa20213033

ABSTRACT.
In this paper, we are interested in the initial value problem for the pseudo-parabolic equation with non-local terms. This problem has many applications in the fields of science and technology. The first results of the paper are related to the existence and regularity  of the solution. We propose  Banach’s fixed point theorem to show the main results. The regularity estimates of the first order derivative according to time variable  is also examined. The second result is that we prove that the solution of the pseudo-parabolic equation converges to the solution of the parabolic equation with a sufficiently strong smoothness of the initial data.

 AMS (MOS) Subject Classification. 39A10.