Results 1 to 2 of 2

Math Help - Partial Differential Equations questions

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    1

    Exclamation Partial Differential Equations questions

    Hey I have these problems that I'm having trouble with for my PDE class. A complete solution would be nice but any sort of direction would be greatly appreciated. Also I'm not sure if I'm supposed to post multiple problems but anyways...

    1. find u(r,theta) when r is equivalent to sqrt(x(1)^2+x(2)^2) less than or equal to 2
    laplacian of u equals zero, in r less than or equal to 2
    u(2,theta)=cos(3*theta) when 0 <theta<2pi

    2.find all u(x)=u(x1,x2) in 0<x1<2; -1<x2<1 when laplacian of u equals zero
    BCs are du/dx1(0,x2)=du/dx2(2,x2)=0 for previous constraints on x1, x2
    du/dx2(x1,1)=1+cos(3*(x2))
    du/dx2(x1,-1)=1+cos(3*(x2))

    3.let u(x,t); x in R^1, t>0 satisfy
    u_tt - u_xx +2u_x +3u = 0; u(x,0)=f(x); u_t(x,0)=g(x)
    Let uhat(xi,t)=1/sqrt(2pi) * integral from -inf to +inf (exp[-i*xi*x]*u(x,t)dx) be the fourier transform of u wrt x
    i)find uhat(xi,t) in terms of fhat(xi) and ghat(xi)
    ii)Give an integral for u(x,t) in terms of fhat(xi) and ghat(xi), don't evaluate integral

    4. find u(x,t)=u(x1,x2,x3,t) for x in R^3, t>0 if
    u_tt - laplacian u = 0; u(x,0) = 0; u_t(x,0)=aX_2(x) which is equivalent to a if |x|<2 and 0 if |x|>2.
    i)give an explicit formula(s) in simplest terms for u. Evaluate any integrals.
    ii)give all values of t for which u(0,0,5,t) does not equal 0

    5. find the solution u(x,t), x in R^3, t>0 to
    u_tt - c^2 * laplacian u = del(x1)del(x2)del(x3)del(t)
    u(x,0)=0
    u_t(x,0)=0
    Evaluate all integrals to get the fundamental solution of this equation.

    Again sorry if i'm not supposed to post more than one problem at a time, any help would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by JCln24 View Post
    Hey I have these problems that I'm having trouble with for my PDE class. A complete solution would be nice but any sort of direction would be greatly appreciated. Also I'm not sure if I'm supposed to post multiple problems but anyways...

    1. find u(r,theta) when r is equivalent to sqrt(x(1)^2+x(2)^2) less than or equal to 2
    laplacian of u equals zero, in r less than or equal to 2
    u(2,theta)=cos(3*theta) when 0 <theta<2pi

    2.find all u(x)=u(x1,x2) in 0<x1<2; -1<x2<1 when laplacian of u equals zero
    BCs are du/dx1(0,x2)=du/dx2(2,x2)=0 for previous constraints on x1, x2
    du/dx2(x1,1)=1+cos(3*(x2))
    du/dx2(x1,-1)=1+cos(3*(x2))

    3.let u(x,t); x in R^1, t>0 satisfy
    u_tt - u_xx +2u_x +3u = 0; u(x,0)=f(x); u_t(x,0)=g(x)
    Let uhat(xi,t)=1/sqrt(2pi) * integral from -inf to +inf (exp[-i*xi*x]*u(x,t)dx) be the fourier transform of u wrt x
    i)find uhat(xi,t) in terms of fhat(xi) and ghat(xi)
    ii)Give an integral for u(x,t) in terms of fhat(xi) and ghat(xi), don't evaluate integral

    4. find u(x,t)=u(x1,x2,x3,t) for x in R^3, t>0 if
    u_tt - laplacian u = 0; u(x,0) = 0; u_t(x,0)=aX_2(x) which is equivalent to a if |x|<2 and 0 if |x|>2.
    i)give an explicit formula(s) in simplest terms for u. Evaluate any integrals.
    ii)give all values of t for which u(0,0,5,t) does not equal 0

    5. find the solution u(x,t), x in R^3, t>0 to
    u_tt - c^2 * laplacian u = del(x1)del(x2)del(x3)del(t)
    u(x,0)=0
    u_t(x,0)=0
    Evaluate all integrals to get the fundamental solution of this equation.

    Again sorry if i'm not supposed to post more than one problem at a time, any help would be greatly appreciated.
    This look like part of an assignment that will count towards your final grade. MHF policy is to not knowingly help with such questions.

    Thread closed (you can pm me and discuss this if you wish).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. partial differential equations
    Posted in the Differential Equations Forum
    Replies: 7
    Last Post: January 13th 2010, 11:31 AM
  2. Partial Differential Equations
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: December 10th 2009, 02:28 PM
  3. Partial Differential Equations
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: September 2nd 2009, 05:58 PM
  4. partial differential equations
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: April 9th 2009, 06:56 AM
  5. Partial Differential Equations
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 11th 2007, 01:38 PM

Search Tags


/mathhelpforum @mathhelpforum