Three-dimensional mathematical problems of thermoelasticity of anisotropic bodies. I.
We prove that strong solutions of the Boussinesq equations in 2D and 3D can be extended as analytic functions of complex time. As a consequence we obtain the backward uniqueness of solutions.
We give necessary and sufficient conditions on the initial data such that the solutions of parabolic equations have a prescribed Sobolev regularity in time and space.
In this paper, we study the time asymptotic behavior of the solution to an abstract Cauchy problem on Banach spaces without restriction on the initial data. The abstract results are then applied to the study of the time asymptotic behavior of solutions of an one-dimensional transport equation with boundary conditions in -space arising in growing cell populations and originally introduced by M. Rotenberg, J. Theoret. Biol. 103 (1983), 181–199.
The role of time delays in solid avascular tumour growth is considered. The model is formulated in terms of a reaction-diffusion equation and mass conservation law. Two main processes are taken into account-proliferation and apoptosis. We introduce time delay first in underlying apoptosis only and then in both processes. In the absence of necrosis the model reduces to one ordinary differential equation with one discrete delay which describes the changes of tumour radius. Basic properties of the...