A closed form solution to one dimensional robin boundary problems

作者：Yang, Chang li; Zhu, Ai lin^*

来源：Acta Mathematicae Applicatae Sinica-English Series, 2012, 28(3): 549-556.

DOI：10.1007/s10255-012-0156-4

• partial differential equations
• Robin boundary problem
• diffusion processes
• Girsanov's formula

Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). In this paper, we will use reflected and absorbed Brownian motion and stochastic differential equations to construct a closed form solution to one dimensional Robin boundary problems. Meanwhile, we will give a reasonable explanation to the closed form solution from a stochastic point of view. Finally, we will extend the problem to Robin boundary problem with two boundary conditions and give a specific solution by resorting to a stopping time.

• 出版日期2012-7
• 单位华东师范大学