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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.