Non-simultaneous Blow-up For Heat Equations With Positive-Negative Sources And Coupled Boundary Fluxes

This paper studies non-simultaneous blow-up for a nonlinear heat system with positivenegative sources and coupled boundary fluxes. At first, the critical exponent is establishedvia a complete classification to the six nonlinear parameters. The main attention of thepaper is contributed to non-simultaneous blow-up phenomena of solutions in the one-dimension case. The sufficient-necessary conditions are determined for non-simultaneousblowing up with suitable initial data. In particular, some sufficient conditions are obtainedunder which any blow-up must be non-simultaneous.In the introduction, we give the background to the subject of the paper. The primary tools used in this paper are stated in Chapter 2, and then the blow-up criteria areestablished in Chapter 3. In Chapter 4, by using the scaling method and the fundermental solution method, we obtain the conditions for non-simultaneousblowing up. The lastsection is a discussion to the main results of the paper.