arXiv subjects
Publications and source records attributed to Jimyeong Lee.
We prove local existence for classical solutions of a free boundary problem which arises in one of the biological selection models proposed by Brunet and Derrida, [2] and Durrett and Remenik, [14]. The problem we consider describes the limit evolution of branching brownian particles on the line with death of the leftmost particle at each creation time as studied in [12]. We use extensively results in [5] and [15].
We prove that for a standard Brownian motion, there exists a first-passage-time density function through a locally Hölder continuous curve with exponent greater than 1/2. By using a property of local time of a standard Brownian motion and the theories of partial differential equations in Cannon [2], we find a sufficient condition for existence of the density function. We also show that this density function is proportional to the space derivative of the Green function of the heat equation with Dirichlet boundary condition at the moving boundary.
We prove local existence for classical solutions of a free boundary problem which arises in one of the biological selection models proposed by Brunet and Derrida, [3]. The problem we consider describes the limit evolution of branching brownian particles on the line with death of the leftmost particle at each creation time as studied in [7]. We use extensively results in [1] and [2].