A numerical investigation of blow-up in the moving heat source problems in two-dimensions

作者：Zhu Hancan^*; Liang Kewei

来源：WSEAS Transactions on Mathematics, 2013, 12(3): 286-295.

• Absorbing boundary condition
• Blow-up
• Collocation method
• Moving heat sources
• Moving mesh method
• Reaction diffusion equations

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 a circle which is allowed to move. By using the coordinate transformation, the equation is simplified to a one-dimensional one. Then it is solved by the moving collocation method. The numerical results show that the blow-up occurs if the speed of the heat source is slow, and the blow-up is avoided when the heat source moves fast enough.

• 出版日期2013