While the abstract theory available can be applied directly to problems with unbounded domains or zero boundary conditions, many problems arising in applications are in fact initial–boundary value ...

Madalina Deaconu *†, Samuel Herrmann ‡, INITIAL-BOUNDARY VALUE PROBLEM FOR THE HEAT EQUATION—A STOCHASTIC ALGORITHM, The Annals of Applied Probability, Vol. 28, No. 3 (June 2018), pp. 1943-1976 ...