NONLOCAL CONVECTION-DIFFUSION VOLUME-CONSTRAINED PROBLEMS AND JUMP PROCESSES

作者：Du Qiang^*; Huang Zhan; Lehoucq Richard B

来源：Discrete and Continuous Dynamical Systems-Series B, 2014, 19(2): 373-389.

DOI：10.3934/dcdsb.2014.19.373

• Nonlocal
• convection-diffusion
• maximum principle
• volume-constrained problem
• master equation
• Monte Carlo

We introduce the Cauchy and time-dependent volume-constrained problems associated with a linear nonlocal convection-diffusion equation. These problems are shown to be well-posed and correspond to conventional convection-diffusion equations as the region of nonlocality vanishes. The problems also share a number of features such as the maximum principle, conservation and dispersion relations, all of which are consistent with their corresponding local counterparts. Moreover, these problems are the master equations for a class of finite activity Levy-type processes with nonsymmetric Levy measure. Monte Carlo simulations and finite difference schemes are applied to these nonlocal problems, to show the effects of time, kernel, nonlocality and different volume-constraints.

• 出版日期2014-3