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 ...

In this paper, the combination of conduction with radiation into a semitransparent medium which includes absorption, emission and scattering has been investigated. In order to Study the conduction in medium, the Non-Fourier heat conduction has been applied. In this model there is a time delay between heat flux and temperature gradient. Also, in contrast with Fourier heat conduction, the speed o...

The thermal problem of this note was solved with the hope of using it to try to test the theory that the earth was formed by accretion on the dust cloud hypothesis;1 but there are many uncertain and unknown physical factors involved and, on reflection, it seems that the contemplated thermal considerations are unable at present to help in drawing conclusions. However, it is hoped that the follow...

in this paper, we consider an inverse problem of linear heat equation with nonlinear boundary condition. we identify the temperature and the unknown radiation tern from an overspecified condition on the boundary