Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Hyperbolic_partial_differential_equation> ?p ?o. }
Showing items 1 to 40 of
40
with 100 items per page.
- Hyperbolic_partial_differential_equation abstract "In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first n−1 derivatives. More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic hypersurface. Many of the equations of mechanics are hyperbolic, and so the study of hyperbolic equations is of substantial contemporary interest. The model hyperbolic equation is the wave equation. In one spatial dimension, this isThe equation has the property that, if u and its first time derivative are arbitrarily specified initial data on the initial line t = 0 (with sufficient smoothness properties), then there exists a solution for all time.The solutions of hyperbolic equations are "wave-like." If a disturbance is made in the initial data of a hyperbolic differential equation, then not every point of space feels the disturbance at once. Relative to a fixed time coordinate, disturbances have a finite propagation speed. They travel along the characteristics of the equation. This feature qualitatively distinguishes hyperbolic equations from elliptic partial differential equations and parabolic partial differential equations. A perturbation of the initial (or boundary) data of an elliptic or parabolic equation is felt at once by essentially all points in the domain.Although the definition of hyperbolicity is fundamentally a qualitative one, there are precise criteria that depend on the particular kind of differential equation under consideration. There is a well-developed theory for linear differential operators, due to Lars Gårding, in the context of microlocal analysis. Nonlinear differential equations are hyperbolic if their linearizations are hyperbolic in the sense of Gårding. There is a somewhat different theory for first order systems of equations coming from systems of conservation laws.".
- Hyperbolic_partial_differential_equation wikiPageExternalLink lpdetoc2.pdf.
- Hyperbolic_partial_differential_equation wikiPageExternalLink npde-toc2.pdf.
- Hyperbolic_partial_differential_equation wikiPageExternalLink S0273-0979-00-00868-5.pdf.
- Hyperbolic_partial_differential_equation wikiPageID "1575825".
- Hyperbolic_partial_differential_equation wikiPageRevisionID "605287893".
- Hyperbolic_partial_differential_equation first "B.L.".
- Hyperbolic_partial_differential_equation hasPhotoCollection Hyperbolic_partial_differential_equation.
- Hyperbolic_partial_differential_equation id "H/h048300".
- Hyperbolic_partial_differential_equation id "p/h048310".
- Hyperbolic_partial_differential_equation last "Rozhdestvenskii".
- Hyperbolic_partial_differential_equation title "Hyperbolic partial differential equation, numerical methods".
- Hyperbolic_partial_differential_equation subject Category:Hyperbolic_partial_differential_equations.
- Hyperbolic_partial_differential_equation type Abstraction100002137.
- Hyperbolic_partial_differential_equation type Communication100033020.
- Hyperbolic_partial_differential_equation type DifferentialEquation106670521.
- Hyperbolic_partial_differential_equation type Equation106669864.
- Hyperbolic_partial_differential_equation type HyperbolicPartialDifferentialEquations.
- Hyperbolic_partial_differential_equation type MathematicalStatement106732169.
- Hyperbolic_partial_differential_equation type Message106598915.
- Hyperbolic_partial_differential_equation type PartialDifferentialEquation106670866.
- Hyperbolic_partial_differential_equation type Statement106722453.
- Hyperbolic_partial_differential_equation comment "In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first n−1 derivatives. More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic hypersurface. Many of the equations of mechanics are hyperbolic, and so the study of hyperbolic equations is of substantial contemporary interest.".
- Hyperbolic_partial_differential_equation label "Ecuación hiperbólica en derivadas parciales".
- Hyperbolic_partial_differential_equation label "Equazione differenziale alle derivate parziali iperbolica".
- Hyperbolic_partial_differential_equation label "Equação hiperbólica em derivadas parciais".
- Hyperbolic_partial_differential_equation label "Hyperbolic partial differential equation".
- Hyperbolic_partial_differential_equation label "Гиперболические уравнения".
- Hyperbolic_partial_differential_equation label "双曲型偏微分方程式".
- Hyperbolic_partial_differential_equation sameAs Ecuación_hiperbólica_en_derivadas_parciales.
- Hyperbolic_partial_differential_equation sameAs Équation_aux_dérivées_partielles_hyperbolique.
- Hyperbolic_partial_differential_equation sameAs Equazione_differenziale_alle_derivate_parziali_iperbolica.
- Hyperbolic_partial_differential_equation sameAs 双曲型偏微分方程式.
- Hyperbolic_partial_differential_equation sameAs Equação_hiperbólica_em_derivadas_parciais.
- Hyperbolic_partial_differential_equation sameAs m.05cqmt.
- Hyperbolic_partial_differential_equation sameAs Q2627459.
- Hyperbolic_partial_differential_equation sameAs Q2627459.
- Hyperbolic_partial_differential_equation sameAs Hyperbolic_partial_differential_equation.
- Hyperbolic_partial_differential_equation wasDerivedFrom Hyperbolic_partial_differential_equation?oldid=605287893.
- Hyperbolic_partial_differential_equation isPrimaryTopicOf Hyperbolic_partial_differential_equation.