In this paper, a class of nonlinear heat‐conduction equations is derived. The properties of these heat‐conduction equations are analyzed. It is shown that the solutions of these equations contain singularity. That is, when T = Tm, discontinuity, i.e. blown‐up, occurs to the solutions. The occurrence of the blown‐ups is closely related the abnormal distribution of the initial ground temperatures, and so there might be some connections between blown‐ups and earthquakes.
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