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This paper studies the numerical solutions of semilinear parabolic partial differential equations (PDEs) on unbounded spatial domains whose solutions blow up in finite time. There are two major difficulties usually in numerical solutions: the singularity of blow-up and the unboundedness. We propose local absorbing boundary conditions (LABCs) on the selected… (More)

- Kewei Liang, Ping Lin
- 2005

We present a splitting moving mesh method for multi-dimensional reaction-diffusion problems with nonlinear forcing terms over rectangular domains. The structure of the adaptive algorithm is an elegant combination of an operator splitting and one-dimensional moving mesh. It is motivated by the nature of splitting method, which splits a multi-dimensional… (More)

- K Kunisch, K Liang, X Lu, Karl Kunisch, Kewei Liang
- 2014

This work is devoted to stationary optimal control problems with polygonal constraints on the components of the state. Existence of Lagrange multipliers, of different regularity, is verified for the cases with and without Slater condition holding. For the numerical realization a semi-smooth Newton method is proposed for an appropriately chosen family of… (More)

- Hancan Zhu, Kewei Liang
- 2013

The temperature of a combustible material will rise or even blow up when a heat source moves across it. In this paper, we study the blow-up phenomenon in this kind of moving heat source problems in two-dimensions. First, a two-dimensional heat equation with a nonlinear source term is introduced to model the problem. The nonlinear source is localized around… (More)

This work is devoted to stationary optimal control problems with polygonal constraints on the components of the state. Existence of Lagrange multipliers, of different regularity, is verified for the cases with and without Slater condition holding. For the numerical realization a semi-smooth Newton method is proposed for an appropriately chosen family of… (More)

- K Kunisch, L Kewei, L Xiliang, Kunisch Karl, Kewei Liang
- 2009

This work is devoted to stationary optimal control problems with polygonal constraints on the components of the state. Existence of Lagrange multipliers, of different regularity, is verified for the cases with and without Slater condition holding. For the numerical realization a semi-smooth Newton method is proposed for an appropriately chosen family of… (More)