Derivation and mathematical study of a sorption-coagulation equation

作者：Hingant Erwan^*; Sepulveda Mauricio

来源：Nonlinearity, 2015, 28(10): 3623-3661.

DOI：10.1088/0951-7715/28/10/3623

• polymers
• metal ions
• coagulation equation
• existence of solutions
• finite volume scheme
• weak stability
• partial differential equation

This paper deals with the derivation and mathematical study of a new model of interactions between chemical polymers and metal ions. The equation describes the evolution of the distribution f (t, p, q) of all polymers at time t >= 0 in a given configuration (p, q), belonging to a set of admissible configurations S. Variable p being the size of the polymer and q the number of metal ions they captured through sorption. The model consists of a nonlinear transport term in the q variable and a quadratic source term, a two-dimensional coagulation operator in both variables p and q. We formally derive the model from considerations on microscopic chemical processes. Next, we prove the existence of solutions for all time and we build a finite volume scheme. We prove that the sequence of approximated solutions is convergent, thanks to a L-1 - weak stability principle. Finally, we illustrate and discuss the long-time behaviour of the solutions.

• 出版日期2015-10