Blow-up Theories for Semilinear Parabolic Equations

From the reviews: "The book approaches the blow-up theories for semilinear parabolic equations using maximum principles and a priori estimates. ... this book is an excellent mathematical monograph and a valuable reference for researchers in the field of nonlinear partial differential equations. This book also clearly benefits instructors who need a solid and updated text for a topic course in partial differential equations. The author has produced a commendable work of scholarly achievement." (Hongwei Chen, Mathematical Reviews, Issue 2012 i) "These lecture notes are intended for graduate students ... of basic theory of second-order parabolic and elliptic equations. ... At the end of each chapter, there is a set of well-chosen exercises. ... It is a nice addition to the existing literature on blow-up since the previous books were mostly intended for more advanced readers." (Marek Fila, Zentralblatt MATH, Vol. 1226, 2012)

• 1 Introduction.- 2 A review of elliptic theories.- 3 A review of parabolic theories.- 4 A review of fixed point theorems.-5 Finite time Blow-up for evolution equations.- 6 Steady-State solutions.- 7 Blow-up rate.- 8 Asymptotically self-similar blow-up solutions.- 9 One space variable case