Some Properties Of The Solutions For Several Local Or Nonlocal Parabolic Systems

In this thesis, we will discuss global blow-up for a localized nonlinear parabolic system with a nonlocal boundary conditions% weak solution for parabolic system with nonstandard growth conditions and blow-up for a nonlinear degenerate parabolic equation with variable exponents.This thesis was divided into five chapters, in the first two chapters, we present introduction and some basic knowledge, in the third, fourth and fifth chapter, we separately consider the following systemIn the third chapter of this thesis, we consider the properties of positive solutions for a nonlinear parabolic system with a localized reaction source and a nonlocal boundary condition (3.1). In this chapter, we use the Souplet’s method to obtain the existence of the positive solution with localized reaction source, by using the super-solution and sub-solution method to establish the global existence and finite time blow-up of the positive solution for a nonlinear parabolic system.In the fourth chapter, we discuss the weak solution for parabolic system with nonstandard growth conditions (4.1). We applied the method of parabolic regularization to prove the existence of weak solutions to the problems mentioned above. By making a sequence of estimates to weak solutions, we proved the weak convergence of the approximation solution sequence and justified the existence of weak solutions.In the fifth chapter, we study a nonlinear parabolic system with variable reactions (5.1). In this chapter, we establish the existence-uniqueness with comparison principle of local solutions to the regularized problem, and then by using the method of super-solution and sub-solution, establish the global existence and finite time blow-up of the positive solution for a nonlinear parabolic system.