2021/06/03 by Chen Cui, Chen, Cui, Jiahui Hong +3
Mathematics · Medicine · Biochemistry, Genetics and Molecular Biology · #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Sphingolipid Metabolism and Signaling
paper · pdf · doi:10.48550/arxiv.2106.01546
The main purpose of this paper is to study the global propagation of singularities of viscosity solution to discounted Hamilton-Jacobi equation λv(x)+H( x, Dv(x) )=0 , x∈ ℝn. We reduce the problem for equation \eqrefeq:discount 1 into that for a time-dependent evolutionary Hamilton-Jacobi equation. We proved that the singularities of the viscosity solution of \eqrefeq:discount 1 propagate along locally Lipschitz singular characteristics which can extend to +∞. We also obtained the homotopy equivalence between the singular set and the complement of associated the Aubry set with respect to the viscosity solution of equation \eqrefeq:discount 1.