In this paper, we study a parabolic system with general singular terms and positive Dirichlet boundary conditions. Some sufficient conditions for finite-time quenching and global existence of the solutions are obtained, and the blow-up of time-derivatives at the quenching point is verified. Furthermore, under some appropriate hypotheses, we prove that the quenching point is only origin and quenching of the system is non-simultaneous. Moreover, the estimate of quenching rate of the corresponding solution is established in this article.
Abstract:In order to solve the vehicle routing problem, this paper introduces the Gauss mutation, which is based on the common particle swarm algorithm, to constitute an improved particle swarm algorithm (NPSO). In the process of solving vehicle routing problem, the NPSO is encoded by integer and proposes a new way to adjust the infeasible solutions. The particles are divided into two overlapping subgroups, and join the two-two exchange neighborhood search to iterate. Finally, the simulation experiments show that the proposed algorithm can get the optimal solution faster and better, and it has a certain validity and practicability.
Abstract:In this paper, we investigate a diffusion system of two parabolic equations with more general singular coupled boundary fluxes. Within proper conditions, we prove that the finite quenching phenomenon happens to the system. And we also obtain that the quenching is non-simultaneous and the corresponding quenching rate of solutions. This extends the original work by previous authors for a heat system with coupled boundary fluxes subject to non-homogeneous Neumann boundary conditions.
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