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searching for Initial value problem 67 found (142 total)

Cauchy boundary condition (627 words) [view diff] no match in snippet view article find links to article

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

Heinz-Otto Kreiss (378 words) [view diff] exact match in snippet view article find links to article

died in Stockholm in 2015, aged 85. Kreiss did research on the initial value problem for partial differential equations, numerical treatment of partial

James W. York (276 words) [view diff] exact match in snippet view article find links to article

Carolina State University. York used conformal geometry in the initial value problem, and introduced concepts now called the York curvature and York

Duhamel's principle (1,978 words) [view diff] exact match in snippet view article find links to article

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

Beam propagation method (985 words) [view diff] no match in snippet view article find links to article

(for the waveguide axis) and they can be solved as "initial" value problem. The "initial" value problem does not involve time, rather it is for the spatial

Hadamard's method of descent (266 words) [view diff] exact match in snippet view article find links to article

wave equation, the heat equation and other versions of the Cauchy initial value problem. As Hadamard (1923) wrote: We thus have a first example of what

Carathéodory's existence theorem (1,138 words) [view diff] exact match in snippet view article find links to article

( t , t 0 , y 0 ) {\displaystyle y(t)=y(t,t_{0},y_{0})} to the initial value problem y ′ ( t ) = f ( t , y ( t ) ) , y ( t 0 ) = y 0 . {\displaystyle

Heat equation (9,874 words) [view diff] exact match in snippet view article find links to article

2010)). In one variable, the Green's function is a solution of the initial value problem (by Duhamel's principle, equivalent to the definition of Green's

Ultrahyperbolic equation (568 words) [view diff] exact match in snippet view article find links to article

and Steven Weinstein proved that under a nonlocal constraint, the initial value problem is well-posed for initial data given on a codimension-one hypersurface

Zero stability (351 words) [view diff] exact match in snippet view article find links to article

refers to the stability of a numerical scheme applied to the simple initial value problem y ′ ( x ) = 0 {\displaystyle y'(x)=0} . A linear multistep method

Parabolic partial differential equation (1,149 words) [view diff] no match in snippet view article find links to article

{\displaystyle u_{t}=Lu} (note the absence of a minus sign). An initial-value problem for the backward heat equation, { u t = − Δ u on Ω × ( 0 , T

Luis Vega (mathematician) (384 words) [view diff] exact match in snippet view article

Iberoamericana (since 2011). In 2006 Vega was Invited Speaker with talk The initial value problem for nonlinear Schrödinger equations at the International Congress

Flow (mathematics) (2,679 words) [view diff] exact match in snippet view article

{\boldsymbol {x}}:\mathbb {R} \to \mathbb {R} ^{n}} ⁠ the solution of the initial value problem x ˙ ( t ) = F ( x ( t ) ) , x ( 0 ) = x 0 . {\displaystyle {\dot

Hitoshi Ishii (438 words) [view diff] exact match in snippet view article find links to article

"偏微分方程式の初期値問題のLP可解性及び一意性" (translation: "Lp solvability and uniqueness of the initial value problem for partial differential equations"). He became an assistant professor

Green's function (5,191 words) [view diff] no match in snippet view article find links to article

{\displaystyle \delta } is Dirac's delta function; the solution of the initial-value problem L y = f {\displaystyle Ly=f} is the convolution ( G ∗ f {\displaystyle

Fourier integral operator (681 words) [view diff] exact match in snippet view article find links to article

of Fourier integral operators is the solution operator for the initial value problem for the wave operator. Indeed, consider the following problem: 1

Integral curve (822 words) [view diff] exact match in snippet view article find links to article

that α is a local solution to the ordinary differential equation/initial value problem α ( t 0 ) = p ; α ′ ( t ) = X ( α ( t ) ) . {\displaystyle {\begin{aligned}\alpha

Caratheodory-π solution (748 words) [view diff] exact match in snippet view article find links to article

control, u = g ( x , t ) {\displaystyle u=g(x,t)} . Then, given an initial value problem, Ross partitions the time interval [ 0 , ∞ ) {\displaystyle [0,\infty

Differential inclusion (1,072 words) [view diff] exact match in snippet view article find links to article

closed, convex set for all t and x. Existence of solutions for the initial value problem d x d t ( t ) ∈ F ( t , x ( t ) ) , x ( t 0 ) = x 0 {\displaystyle

Shape dynamics (1,047 words) [view diff] exact match in snippet view article find links to article

fixed in such a way that its initial value problem and its equations of motion coincide with the initial value problem and equations of motion of the

Hiroshi Fujita (524 words) [view diff] exact match in snippet view article find links to article

(1962), 243–260. Hiroshi Fujita and Tosio Kato. On the Navier-Stokes initial value problem. I. Arch. Rational Mech. Anal. 16 (1964), 269–315. Hiroshi Fujita

Multiple time dimensions (1,070 words) [view diff] exact match in snippet view article find links to article

giving it the metric signature (10,2). The existence of a well-posed initial value problem for the ultrahyperbolic equation (a wave equation in more than one

Jean Bourgain (1,523 words) [view diff] exact match in snippet view article find links to article

group theory. He proved the uniqueness of the solutions for the initial value problem of the Korteweg–De Vries equation. He formulated what became known

James Serrin (488 words) [view diff] case mismatch in snippet view article find links to article

MR 0106646, S2CID 120478897, Zbl 0089.19103. Serrin, James (1963), "The initial Value problem for the Navier-Stokes equations", in Langer, Rudolph E. (ed.), Nonlinear

Spacetime triangle diagram technique (2,908 words) [view diff] exact match in snippet view article find links to article

\;x_{3}=z\right\}} separation of the spatial variables result in the initial value problem for a hyperbolic PDE known as the 1D Klein–Gordon equation (KGE)

Variation of parameters (3,989 words) [view diff] no match in snippet view article find links to article

obtained in this manner, for s going between 0 and t. The homogeneous initial-value problem, representing a small impulse F ( s ) d s {\displaystyle F(s)\,ds}

Cole–Hopf transformation (620 words) [view diff] no match in snippet view article find links to article

Cole-Hopf transformation. With the transformation, the following initial-value problem can now be solved: w t − a Δ w = 0 , w ( 0 , x ) = e − b g ( x )

John Moffat (physicist) (2,249 words) [view diff] case mismatch in snippet view article

1177–1184. (1993) "Superluminary Universe: A Possible Solution to the Initial Value Problem in Cosmology," Int. Jour. Mod. Phys. D2: 351–366. (1995) "Nonsymmetric

Straightening theorem for vector fields (441 words) [view diff] exact match in snippet view article find links to article

Let Φ ( t , p ) {\displaystyle \Phi (t,p)} be the solution of the initial value problem x ˙ = f ( x ) , x ( 0 ) = p {\displaystyle {\dot {x}}=f(x),x(0)=p}

Richard P.A.C. Newman (432 words) [view diff] exact match in snippet view article find links to article

Online at JSTOR (accessed 17 February 2008) Discusses the Cauchy initial value problem for barotropic perfect fluid cosmological models with conformal

Mathematics of general relativity (7,044 words) [view diff] exact match in snippet view article find links to article

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

Strang splitting (743 words) [view diff] exact match in snippet view article find links to article

coefficient matrices, then the exact solution to the associated initial value problem would be y ( t ) = e ( L 1 + L 2 ) t y 0 {\displaystyle

Gigliola Staffilani (1,063 words) [view diff] exact match in snippet view article find links to article

Institutions Stanford University Brown University MIT Thesis The initial value problem for some dispersive differential equations (1995) Doctoral advisor

Newton's law of cooling (2,860 words) [view diff] no match in snippet view article find links to article

transfer (SI unit: second − 1 {\displaystyle ^{-1}} ). Solving the initial-value problem using separation of variables gives T ( t ) = T env + ( T ( 0 )

Valentina Borok (1,081 words) [view diff] exact match in snippet view article find links to article

proved the theorem on uniqueness and well-posedness theorems for the initial value problem as well as the Cauchy problem for system of linear partial differential

Pseudo-spectral method (2,505 words) [view diff] no match in snippet view article find links to article

using fast algorithms such as the fast Fourier transform. Take the initial-value problem i ∂ ∂ t ψ ( x , t ) = [ − ∂ 2 ∂ x 2 + V ( x ) ] ψ ( x , t ) , ψ

Steven Weinstein (philosopher) (639 words) [view diff] exact match in snippet view article

a joint paper with Walter Craig, they gave the first well-posed initial value problem for the wave equation in more than one time dimension (the ultrahyperbolic

Continuous simulation (1,489 words) [view diff] exact match in snippet view article find links to article

problem of solving the ODEs for a given initial state is called the initial value problem. In very few cases these ODEs can be solved in a simple analytic

Hans Weinberger (548 words) [view diff] exact match in snippet view article find links to article

Diaz, J. B.; Weinberger, H. F. (1953). "A solution of the singular initial value problem for the Euler-Poisson-Darboux equation". Proc. Amer. Math. Soc.

Mach's principle (3,126 words) [view diff] no match in snippet view article find links to article

Modern relativists see the imprints of Mach's principle in the initial-value problem. Essentially, we humans seem to wish to separate spacetime into

Variable speed of light (2,600 words) [view diff] case mismatch in snippet view article find links to article

John (1993). "Superluminary Universe: A Possible Solution to the Initial Value Problem in Cosmology". International Journal of Modern Physics D. 2 (3):

Kolmogorov equations (1,438 words) [view diff] no match in snippet view article find links to article

{\displaystyle i} , the Kolmogorov forward equations describe an initial-value problem for finding the probabilities of the process, given the quantities

Adaptive step size (1,638 words) [view diff] exact match in snippet view article find links to article

their superior convergence and stability properties. Consider the initial value problem y ′ ( t ) = f ( t , y ( t ) ) , y ( a ) = y a {\displaystyle y'(t)=f(t

Stochastic differential equation (5,665 words) [view diff] exact match in snippet view article find links to article

[}|Z|^{2}{\big ]}<+\infty .} Then the stochastic differential equation/initial value problem d X t = μ ( X t , t ) d t + σ ( X t , t ) d B t for t ∈ [ 0 ,

Canonical quantum gravity (3,809 words) [view diff] no match in snippet view article find links to article

James W. (1971-06-28). "Gravitational Degrees of Freedom and the Initial-Value Problem". Physical Review Letters. 26 (26): 1656–1658. Bibcode:1971PhRvL

Robin Bullough (989 words) [view diff] exact match in snippet view article find links to article

multi-soliton solutions and gone on to both introduce, and to solve the initial value problem for, the system they called the ‘Reduced Maxwell-Bloch (RMB) Equations’

Hole argument (2,539 words) [view diff] exact match in snippet view article find links to article

same field equations in the original coordinate system. So the initial value problem has no unique solution in general relativity. This is also true

Hisashi Okamoto (438 words) [view diff] exact match in snippet view article find links to article

Mathematical Sciences. Okamoto, H.; Kato, T. (1964). "On the Navier-Stokes initial value problem. I". Archive for Rational Mechanics and Analysis. 16 (4): 269–315

Semigroup (4,714 words) [view diff] exact match in snippet view article find links to article

the above initial/boundary value problem can be interpreted as an initial value problem for an ordinary differential equation on the space X: { u ˙ ( t

Camassa–Holm equation (5,569 words) [view diff] exact match in snippet view article find links to article

2006.55.2710 Camassa, Roberto (2003), "Characteristics and the initial value problem of a completely integrable shallow water equation", Discrete Contin

Lorenz system (5,748 words) [view diff] case mismatch in snippet view article find links to article

Saltzman, Barry (1962). "Finite Amplitude Free Convection as an Initial Value Problem—I". Journal of the Atmospheric Sciences. 19 (4): 329–341. Bibcode:1962JAtS

Boltzmann equation (5,027 words) [view diff] exact match in snippet view article find links to article

Arkeryd, Leif (1972). "On the Boltzmann equation part II: The full initial value problem". Arch. Rational Mech. Anal. 45 (1): 17–34. Bibcode:1972ArRMA..45

Three-wave equation (1,547 words) [view diff] no match in snippet view article find links to article

12133. Kaup, D. J. (1980). "A Method for Solving the Separable Initial-Value Problem of the Full Three-Dimensional Three-Wave Interaction". Studies in

Integral equation (5,605 words) [view diff] exact match in snippet view article find links to article

the following section, we give an example of how to convert an initial value problem (IVP) into an integral equation. There are multiple motivations

Sturm–Liouville theory (4,722 words) [view diff] exact match in snippet view article find links to article

method Shooting methods proceed by guessing a value of λ, solving an initial value problem defined by the boundary conditions at one endpoint, say, a, of the

Method of averaging (4,159 words) [view diff] exact match in snippet view article find links to article

^{2}f^{[2]}(x,t,\varepsilon ).} Besides, we define the following initial value problem to be in the standard form: x ˙ = ε f 1 ( x , t ) + ε 2 f [ 2 ]

First-order partial differential equation (3,130 words) [view diff] exact match in snippet view article find links to article

shrinks with velocity c. These are light cones in space-time. The initial value problem for this equation consists in specifying a level surface S where

Lorentz group (9,875 words) [view diff] exact match in snippet view article find links to article

{\mathcal {L}}=-y\partial _{x}+x\partial _{y}.} The corresponding initial value problem (consider r = ( x , y ) {\displaystyle r=(x,y)} a function of a

Emanuele Foà (2,710 words) [view diff] case mismatch in snippet view article find links to article

ISBN / Date incompatibility (help). Serrin, James (1963), "The initial Value problem for the Navier-Stokes equations", in Langer, Rudolph E. (ed.), Nonlinear

Dario Graffi (2,961 words) [view diff] case mismatch in snippet view article find links to article

ISBN / Date incompatibility (help). Serrin, James (1963), "The initial Value problem for the Navier-Stokes equations", in Langer, Rudolph E. (ed.), Nonlinear

Abstract differential equation (1,944 words) [view diff] exact match in snippet view article find links to article

as a Bochner integral. The problem of finding a solution to the initial value problem d u d t = A ( t ) u + f u ( 0 ) = u 0 ∈ D ( A ) , {\displaystyle

Harold Ralph Lewis (892 words) [view diff] no match in snippet view article find links to article

time-dependent Hamiltonian systems, description of solutions of the initial-value problem for the small-signal response of collisionless plasmas, use of Hamilton's

Euler equations (fluid dynamics) (13,150 words) [view diff] exact match in snippet view article

are a subset of the conservative variables. The solution of the initial value problem in terms of characteristic variables is finally very simple. In

Theta function (14,667 words) [view diff] exact match in snippet view article find links to article

}^{\infty }\delta (x-n)} . General solutions of the spatially periodic initial value problem for the heat equation may be obtained by convolving the initial

Women in physics (8,985 words) [view diff] exact match in snippet view article find links to article

Choquet-Bruhat proves that Einstein field equations can be formulated as an initial value problem (local existence of solutions and uniqueness). 1953: Various authors

Computational anatomy (16,879 words) [view diff] exact match in snippet view article find links to article

demonstration that the Euler–Lagrange equations have a well-posed initial value problem with unique solutions for all time, and with the first results on

Light front quantization (12,723 words) [view diff] exact match in snippet view article find links to article

equation is that the light-front is a characteristic surface for the initial value problem. This means the data on the light front is insufficient to generate