Abstract
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, (Phys. Rev. E 56, 2597D2604, 1997) and Durrett and Remenik, (Ann. Probab. 39, 2043–2078, 2011). 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 De Masi et al. (2017). We use extensively results in Cannon (1984) and Fasano (2008).
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I thank A. De Masi and E. Presutti for useful discussions.
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Lee, J. A Free Boundary Problem with Non Local Interaction. Math Phys Anal Geom 21, 24 (2018). https://doi.org/10.1007/s11040-018-9282-4
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DOI: https://doi.org/10.1007/s11040-018-9282-4