Fundamentals of Continuous Growth Processes in Technology and Nature

Abstract Fundamentals of mathematical modeling of surface growth process are under consideration. Mathematical models of 3D and 2D solids that grow owing to processes of continuous influx of new elements (surfaces and fibers) are proposed. Complete systems of equations and boundary value problems are obtained. A method for solving these boundary value problems is developed. Qualitative conclusions and numerical results concerning the behavior of growing solids are presented.