partial differential equation
111Screened Poisson equation — In mathematics, the screened Poisson equation is the following partial differential equation::left [ abla^2 lambda^2 ight] u(mathbf{r}) = f(mathbf{r})where ² is the Laplace operator, λ is a constant, f is an arbitrary function of position (known… …
112Green's function for the three-variable Laplace equation — The free space Green s function for the three variable Laplace equation is given in terms of the reciprocal distance between two points. That is to say the solution of the equation : abla^2 G(mathbf{x},mathbf{x }) = delta(mathbf{x} mathbf{x }) is …
113Lin-Tsien equation — The Lin Tsien equation is the partial differential equation: 2u {tx}+u xu {xx} u {yy} = 0. , References * Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 138, 1997 …
114Ernst equation — In mathematics, the Ernst equation is the non linear partial differential equation:displaystyle Re(u)(u {rr}+u r/r+u {zz}) = (u r)^2+(u z)^2.It is used to produce exact solutions of Einstein s equations.References*Citation | last1=Zwillinger |… …
115Calogero-Degasperis-Fokas equation — In mathematics, the Calogero Degasperis Fokas equation is the nonlinear partial differential equation:displaystyle u {xxx} frac{1}{8}u x^3 + u xleft(Ae^u+Be^{ u} ight)=0.This equation was named after F. Calogero, A. Degasperis, and A. Fokas.ee… …
116Generalized Korteweg-de Vries equation — In mathematics the generalized Korteweg de Vries equation harvs last=Tsutsumi|first= Masayoshi|last2= Mukasa|first2= Toshio|last3= Iino|first3= Riichi|year=1970 is the nonlinear partial differential equation:partial t u + partial x^3 u + partial… …
117Kaup–Kupershmidt equation — The Kaup–Kupershmidt equation is the nonlinear fifth order partial differential equation:u t = u {xxxxx}+10u {xxx}u+25u {xx}u x+20u^2u x = frac16 (6u {xxxx}+60uu {xx}+45u x^2+40u^3) x. It is the first equation in a hierarchy of integrable… …
118wave equation — noun Date: 1926 a partial differential equation of the second order whose solutions describe wave phenomena …
119heat equation — Math., Thermodynam. a partial differential equation the solution of which gives the distribution of temperature in a region as a function of space and time when the temperature at the boundaries, the initial distribution of temperature, and the… …
120Laplace equation — Math. the second order partial differential equation indicating that the Laplace operator operating on a given function results in zero. Cf. harmonic (def. 4c). [1835 45; after P. S. LAPLACE] * * * …
