We study a scalar integro-differential conservation law. The equation wasfirst derived in [2] as the slow erosion limit of granular flow. Considering aset of more general erosion functions, we study the initial boundary valueproblem for which one can not adapt the standard theory of conservation laws.We construct approximate solutions with a fractional step method, byrecomputing the integral term at each time step. A-priori L^\infty bounds andBV estimates yield convergence and global existence of BV solutions.Furthermore, we present a well-posedness analysis, showing that the solutionsare stable in L^1 with respect to the initial data.
展开▼
