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There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.

Blowing up (Algebraic geometry) --- Differential equations, Parabolic --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematical Theory --- Geometry, Algebraic. --- Algebraic geometry --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Partial Differential Equations. --- Applications of Mathematics. --- Analysis. --- Engineering --- Engineering analysis --- Mathematical analysis --- Partial differential equations --- 517.1 Mathematical analysis --- Math --- Science --- Geometry --- Differential equations, partial. --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic