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¡¡¡¡Nonlinear evolution equations describe some important partial differential equations which develop over time. Large problems of these equations arise in mathematical models from physics£¬ chemistry and biology. Thus they have a high degree of practical background. In views of mathematical theory and the development in applied sciences£¬ it is very important to study these equations. This book will investigate the blowup phenomena and global well-posedness in nonlinear heat conduction equation and magnetohydrodynamic system£¬ which are arose in applied sciences. The book consists of five parts in the following.¡¡¡¡In Chapter 1£¬ we consider the asymptotic behavior at infinity of the stationary solution which corresponding to a semilinear heat equation with exponential source£¬ and get the behavior of the backward self-similar solution for the heat equation when approaching the blowup time£¬ which provide convenience to study the blowup phenomenon of the singularity solution for the heat equation.¡¡¡¡In Chapter 2£¬ we discuss the nonexistence of type n blowup for heat equation with exponential nonlinearity in the whole space when initial data satisfy some given conditions. Using zero theory and the behavior of stationary solution of heat equation£¬ we give a sufficient condition for the occurrence of type I blowup in the lower supercritical range by intersection comparison principle.¡¡¡¡In Chapter 3£¬ we study the global well-posedness for MHD system with mixed partial dissipation and magnetic diffusion in 2-dimensions. Using energy method£¬ we consider the global well-posedness for mixed partial dissipation£¬ we derive the desired results under some certain condition for the solutions of MHD system.