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Hamilton–Jacobi equations is a specialized mathematics/physics category covering the theory, methods, and applications of first-order nonlinear partial differential equations arising from Hamiltonian mechanics, calculus of variations, and optimal control. Books in this category treat the classical Hamilton–Jacobi formalism and its modern developments: characteristics and classical solutions, viscosity solutions and well-posedness, weak KAM theory and action-minimizing orbits, symplectic and geometric viewpoints, and numerical schemes for front propagation and optimal control problems. They range from rigorous analytic texts for researchers to applied introductions for physicists and engineers, often linking to dynamics, semiclassical limits in quantum mechanics, control theory, and computational methods.

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