Blow-up Analysis For Parabolic Systems With Nonlinearities Of Mixed Types

This paper deals initial-boundary problems for parabolic systems with multiple nonlinear terms of mixed types, i.e., combinations of nonlinearities of power and exponent types. Three kinds of couplings (source-source, flux-flux, source-flux) are considered. The growth of the solutions come from both the sources and the boundary flux. By using the comparison principle, the blow-up criteria are established under different couplings with nonlinear terms of power or exponent types.In the introduction, we introduce the background to the nonlinear parabolic systems. In Chapter 2, we give some basic knowledge to be used in this paper. In Chapter 3, we describe the main results of the paper — the sufficient and necessary conditions for global existence of solutions with different nonlinearities, and then prove them in Chapter 4. In the last chapter, we discuss all the conclusions obtained in this paper.