Special Session 129: Qualitative and Quantitative Techniques for Differential Equations arising in Economics, Finance and Natural Sciences
Contents
We consider a model for the irreversible solidification process of certain materials by taking in consideration the effects of natural convection in molten regions. Such a model consists of a highly nonlinear system of partial differential equations coupled to a doubly nonlinear differential inclusion. The existence of weak-strong solutions for the system is proved, and certain mathematical effects of advection on the regularity of the solutions are discussed.