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In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.
Please introduce links to this page from ; try the Find link tool for suggestions. ( November 2016 ) The mathematical analysis of partial differential equations uses analytical techniques to study partial differential equations .
Inhibitors of PDE can prolong or enhance the effects of physiological processes mediated by cAMP or cGMP by inhibition of their degradation by PDE. [ 13 ] Sildenafil (Viagra) is an inhibitor of cGMP-specific phosphodiesterase type 5 , which enhances the vasodilatory effects of cGMP in the corpus cavernosum and is used to treat erectile ...
PDE-constrained optimization; Perfectly matched layer; Perron method; Petrov–Galerkin method; Phase space method; Poincaré–Lelong equation; Poisson's equation; Population balance equation; Porous medium equation; Potential theory; Primitive equations; Proper orthogonal decomposition; Pseudo-differential operator; Pseudoanalytic function
Broer–Kaup equations; Burgers' equation; Euler equations; Fokker–Planck equation; Hamilton–Jacobi equation, Hamilton–Jacobi–Bellman equation; Heat equation; Laplace's equation
A fundamental question for any PDE is the existence and uniqueness of a solution for given boundary conditions. For nonlinear equations these questions are in general very hard: for example, the hardest part of Yau's solution of the Calabi conjecture was the proof of existence for a Monge–Ampere equation.
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A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent phenomena in, i.a., engineering science, quantum mechanics and financial mathematics.
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