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"Parabolic equations" as a book category denotes works focused on parabolic partial differential equations—time-dependent problems exemplified by the heat and diffusion equations—and their theory, methods, and applications. Such books typically treat existence, uniqueness and regularity of solutions for linear and nonlinear initial–boundary value problems; fundamental solutions and Green’s functions; maximum principles, energy estimates and a priori bounds; semigroup and functional-analytic approaches; long-time behavior and stability; and specialized topics like degenerate/singular parabolic equations, stochastic parabolic PDEs, inverse problems and control. They also frequently cover numerical methods (finite difference, finite element, time-stepping schemes) and model-driven applications in physics, biology, finance and engineering. Intended audiences range from advanced undergraduates and graduate students to researchers and practitioners, and most titles presume a background in real analysis, Sobolev spaces and basic PDE theory.

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