Non-simultaneous Blowing Up For Heat Equations With Multiple Nonlinearities

This paper deals with a system of heat equations with inner absorptions and coupled boundary flux. The critical blow-up exponents are discussed carefully with a complete classification for all the nonlinear parameters in the system, where a precise analysis on the geometry of Ω and the absorption coefficients is necessary for the balance situation. For the one-dimensional case, we determine the necessary and sufficient conditions for non-simultaneous blowing up under proper initial data. Moreover, we obtain the conditions under which any blow-up must be non-simultaneous. Finally, a discussion for the main results of the paper is given to illustrate the characters of the model and compare with those of previous works.In the introduction, we give the background to the study of nonlinear parabolic equations. We state some primary tools related to this paper in Chapter 2, and then consider the blow-up criteria problem in Chapter 3. In Chapter 4, by using the Scaling method and the fundamental solution method, we establish the conditions for non-simultaneous blowing up. At last, in Chapter 5, we discuss the main results of the paper.