hypersurface in the domain. A Cauchy problem can be an initial value problem or a boundary value problem (for this case see also Cauchy boundary condition). It...

differential equations associated with Cauchy initial value problems. A special case was proven by Augustin Cauchy (1842), and the full result by Sofya...

In mathematics, a Cauchy (French: [koʃi]) boundary condition augments an ordinary differential equation or a partial differential equation with conditions...

momentum equation Cauchy–Peano theorem Cauchy principal value Cauchy problem Cauchy product Cauchy's radical test Cauchy–Rassias stability Cauchy–Riemann equations...

In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem (a particular boundary value problem of the theory...

u(t)} of the Cauchy problem ( u ( 0 ) = u 0 {\displaystyle u(0)=u_{0}} ) at the moment of time t > 0 {\displaystyle t>0} . If the Cauchy problem is well posed...

The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the inner product between two vectors in an inner...

named for French mathematician Augustin-Louis Cauchy (1789-1857) due to their relevance for the Cauchy problem of general relativity. Although it is usually...

differentiable with }}f'\in C_{ub}(\mathbb {R} )\}} . Consider the abstract Cauchy problem: u ′ ( t ) = A u ( t ) ,       u ( 0 ) = x , {\displaystyle u'(t)=Au(t)...

conserved. The rigorous mathematical theory is based on solving the Cauchy problem for the evolution equation (here the partial differential Vlasov–Poisson...

gives a value to the normal derivative and the variable itself then it is a Cauchy boundary condition. Summary of boundary conditions for the unknown function...

The Cauchy distribution, named after Augustin-Louis Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as...

usually forms a finite-dimensional Lie algebra. The Cauchy problem (sometimes called the initial value problem) is the attempt at finding a solution to a differential...

theorem Cauchy point Cauchy principal value Cauchy problem Abstract Cauchy problem Cauchy process Cauchy product Cauchy's radical test Cauchy–Rassias...

the initial value problem. Thus, this is an example of such a problem with infinite number of solutions. Also called a Cauchy problem by some authors.[citation...

under which an initial value problem has a unique solution. It is also known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence...

the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two...

would be permitted. In a 1990 paper by Novikov and several others, "Cauchy problem in spacetimes with closed timelike curves", the authors state: The only...

unknowns c1 and c2. Solving this system gives the solution for a so-called Cauchy problem, in which the values at 0 for the solution of the DEQ and its derivative...

important problem in the theory of partial differential equations is to determine sufficient conditions on the vector fields Ai for the Cauchy problem { ∂ u...

0} holds when all data are set to zero. The Cauchy–Kowalevski theorem for Cauchy initial value problems essentially states that if the terms in a partial...

the boundary. Many other boundary conditions are possible, including the Cauchy boundary condition and the mixed boundary condition. The latter is a combination...

well-posed initial value problem for the first n − 1 {\displaystyle n-1} derivatives.[citation needed] More precisely, the Cauchy problem can be locally solved...

mathematics from Brandeis University. His dissertation, The analytic Cauchy problem with singular data, is about singularities in analytic partial differential...

In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions...

below), rather than in the sense of measures. Another example is the Cauchy problem for the wave equation in R1+1: c − 2 ∂ 2 u ∂ t 2 − Δ u = 0 u = 0 , ∂...

Fernando; Klinkhammer, Gunnar; Thorne, Kip S.; Yurtsever, Ulvi (1990). "Cauchy problem in spacetimes with closed timelike curves". Physical Review D. 42 (6):...

possible to go from solutions of the Cauchy problem (or initial value problem) to solutions of the inhomogeneous problem. Consider, for instance, the example...

equations, from interpolation theory to Cauchy integrals on Lipschitz curves, from ergodic theory to inverse problems in electrical prospection. Calderón's...

mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M. Intuitively...