Results 1 to 3 of 3

Math Help - Semilinear Wave Equation - White Noise

  1. #1
    Newbie
    Joined
    Dec 2010
    Posts
    2

    Semilinear Wave Equation - White Noise

    Hello!

    I am required to do a paper on the Semilinear Wave Equation as part of a Stochastic Partial Differential Equations seminar.
    The problem is, that I've never taken a course on partial differential equations (only ordinary differential equations) or functional analysis.

    Now I have the following in front of me:

    Let f(s,x,t) and \sigma(s,x,t) be predictable random fields
    depending on the parameters s\in\mathbf{R} and x\in D. We consider
    the initial-boundary value problems for a stochastic wave equation
    as follows

    \frac{\partial^{2}u}{\partial t^{2}}=(\kappa\Delta-\alpha)u+f(u,x,t)+\dot{M}(u,x,t)
    x\in D, t\in(0,T]

    Bu| _{\partial D}=0

    u(x,0)=g(x), \frac{\partial u}{\partial t}(x,0)=h(x)

    where

    \dot{M}(s,x,t)=\sigma(s,x,t)\dot{W}(x,t)

    My problem is now, that I don't understand how this second order differential was constructed.
    What are (\kappa\Delta-\alpha)u, f(u,x,t), \dot{M}(u,x,t) supposed to be here and what has this to do with waves?

    Thank you for your time.
    If you can pinpoint me to some resources, which will make my life easier in understanding this. I will be very thankful!
    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 NoClue View Post
    Hello!

    I am required to do a paper on the Semilinear Wave Equation as part of a Stochastic Partial Differential Equations seminar.
    The problem is, that I've never taken a course on partial differential equations (only ordinary differential equations) or functional analysis.

    Now I have the following in front of me:

    Let f(s,x,t) and \sigma(s,x,t) be predictable random fields
    depending on the parameters s\in\mathbf{R} and x\in D. We consider
    the initial-boundary value problems for a stochastic wave equation
    as follows

    \frac{\partial^{2}u}{\partial t^{2}}=(\kappa\Delta-\alpha)u+f(u,x,t)+\dot{M}(u,x,t)
    x\in D, t\in(0,T]

    Bu| _{\partial D}=0

    u(x,0)=g(x), \frac{\partial u}{\partial t}(x,0)=h(x)

    where

    \dot{M}(s,x,t)=\sigma(s,x,t)\dot{W}(x,t)

    My problem is now, that I don't understand how this second order differential was constructed.
    What are (\kappa\Delta-\alpha)u, f(u,x,t), \dot{M}(u,x,t) supposed to be here and what has this to do with waves?

    Thank you for your time.
    If you can pinpoint me to some resources, which will make my life easier in understanding this. I will be very thankful!
    Why are you attending this seminar when your pre-requisite background is so deficient?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2010
    Posts
    2
    Hello chum !

    I had no alternatives. I was away when the topics for the different seminars were handed out. I had other favorites, but they were already booked out .
    I literally had nothing else to choose from...

    I am reading Oksendals book on SPDE's and am trying to catch up by myself...

    However, I am very thankful, if someone would show me what to do (what material to work through), so I can quickly get to my topic.
    Last edited by NoClue; December 30th 2010 at 01:57 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Difference between Gaussian noise and white Gaussian noise?
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: February 12th 2011, 01:25 AM
  2. Partial differential equation-wave equation(2)
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: September 6th 2009, 09:54 AM
  3. Partial differential equation-wave equation - dimensional analysis
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: August 28th 2009, 12:39 PM
  4. white noise/iid
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 2nd 2009, 06:56 PM
  5. solving semilinear PDE
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: November 27th 2008, 08:53 AM

Search Tags


/mathhelpforum @mathhelpforum