Re: Solving 2nd order PDE into Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg115265] Re: Solving 2nd order PDE into Mathematica*From*: Roland Franzius <roland.franzius at uos.de>*Date*: Thu, 6 Jan 2011 02:02:13 -0500 (EST)*References*: <ig1i9d$6ll$1@smc.vnet.net>

Am 05.01.2011 11:48, schrieb tarpanelli at libero.it: > Hello, > > I saw that DSolve can not solve a 2nd order pde like this > > pde=-D[f[x,t],x]+D[f[x,t],{x,2}]==D[f[x,t],t] > > but I would like to know if someone has already implemented some other > procedure to solve it > The heat/diffusion pde cannot be solved without additonal equations at boundaries (-oo, oo?) and a starting distribution f[x,0] == g[x]. A formal solution eg d_t f = 0, f = a + b e^(-x) is not admissible for physical problems. The equation is probably the radial diffusion equation in dimension 2 and the general solution is an 2-d-integral over a radial symmetric function of r=sqrt(x^2+y^2) only, folded with the two dimensional gaussian kernel (x,y,t; xi,eta,tau) -> 1/( 2 pi (t-tau ) exp(-((x-xi)^2 +(y-eta)^2))/(2 (t-tau)) (t>tau) (constants may differ) -- Roland Franzius