Global Existence And Uniqueness Of Solution For A Fast Reaction-diffusion Equation

This paper is concerned with the global existence and uniqueness of solution fora fast reaction-di?usion equation with conditions for determining solution. In the firstsection, whenα> 0, we show the global existence of solution for the initial-boundaryproblem by the method of upper and lower solution. In the second section, we show theglobal existence and uniqueness of generalized solution for the Cauchy problem by theprolongation of solution.The whole thesis consists of three chapters. In the first chapter, we introduce therelative background knowledge,the development state and the main result. In Chapter 2,we will give the proof of the global existence and uniqueness of generalized solution for theparabolic equation with initial-boundary condition. In Chapter 3, we will give the proofof the global existence and uniqueness of generalized solution for the Cauchy problem.