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Degenerate differential equations --- Differential equations, Elliptic. --- Equations différentielles dégénérées --- Equations différentielles elliptiques --- 51 <082.1> --- Mathematics--Series --- Equations différentielles dégénérées --- Equations différentielles elliptiques --- Degenerate differential equations. --- Algebraic geometry --- Differential equations, Elliptic --- Equations of degenerate type --- Differential equations, Partial --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear

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The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asymptotic behaviour, discretization schemes, coefficient identification, and to introduce relevant solving methods for each of them.

Burgers equation --- Degenerate differential equations --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Burgers equation. --- Degenerate differential equations. --- Equations of degenerate type --- Diffusion equation, Nonlinear --- Heat flow equation, Nonlinear --- Nonlinear diffusion equation --- Nonlinear heat flow equation --- Mathematics. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Calculus of variations. --- Partial Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Applications of Mathematics. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Engineering --- Engineering analysis --- Mathematical analysis --- Partial differential equations --- Math --- Science --- Differential equations, Partial --- Heat equation --- Navier-Stokes equations --- Turbulence --- Differential equations, partial. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Operations research --- Simulation methods --- System analysis