本书为学术专著，对应用科学中提出的非线性热传导方程和磁流体力学方程组的爆破现象及整体适定性进行了研究，介绍了具指数反应源的半线性热方程对应的稳态解在无穷远处的渐近性态，并得到具指数反应源热方程的后向自相似解在趋近于爆破时间的行为，这对研究热方程的奇异解在发生爆破时的性质提供了便利；讨论了全空间中，具指数反应源热方程在超临界情形的初值满足一定条件下爆破的不存在性；研究了具部分耗散和磁流体扩散项的不可压缩磁流体力学方程组的整体适定性问题，利用能量方法，我们考虑了具混合耗散和扩散项磁流体方程组的整体适定性，得到在方程组的解满足一定条件下解的整体适定性。

Chapter 1 Asymptotic Behavior at Infinity of the Stationary Solution to a Semilinear Heat Equation
1.1 Introduction
1.2 The asymptotic behavior at infinity
Chapter 2 Nonexistence of Type II Blowup for Nonlinear Heat Equation with Exponential Nonlinearity
2.1 Introduction
2.2 Preliminary
2.3 Proof of the main results
Chapter 3 Global Well-posedness for MHD System with Mixed Partial Dissipation and Magnetic Diffusion in 2 1/2Dimensions
3.1 Introduction
3.2 Notations and preliminaries
3.3 Global well-posedness for 2 1/2D MHD flows
3.4 Conditional global well-posedness for 2 1/2D MHD flows
Chapter 4 Uniqueness of Weak Solutions to the Boussinesq Equations without Thermal Diffusion
4.1 Preliminaries
4.2 Proof of Theorem 1
4.3 Proof of Theorem 2
4.4 Global existence of weak solutions
Chapter 5 The Resistive Magnetohydrodynamic Equation Near an Equilibrium
5.1 Introduction
5.2 Proof of Theorem
5.3 Proof of Theorem
5.4 Proof of Theorem
References