Blow-up Analysis For Heat Equations With Nonlinear Boundary Flux

This thesis deals with critical exponents and asymptotic behavior of solutions (blow-up rate) to a heat parabolic system coupled via nonlinear flux. By introducing a characteristic algebraic system associated to the problem, we get a clear description on the critical exponents and the asymptotic behavior of solutions, respectively.In the introduction, we give the background to the study of nonlinear parabolic equations. In Chapter 2, we establsh the critical blow-up exponents for the coupled nonlinear parabolic equations, where the so called characteristic algebraic system is introduced. In Chapter 3, we establish the blow-up rates of the problem.