1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Linearity math problem

  1. Mar 19, 2010 #1
    I'm trying to see if [tex]\rho[/tex]utt + EIuxxxx = 0 is linear or non-linear where [tex]\rho[/tex], E and I are constants.

    I got L(u+v) = [tex]\rho[/tex][tex]\delta[/tex]2u2/[tex]\delta[/tex]t2 + EI[tex]\delta[/tex]4u2/[tex]\delta[/tex]x4 + [tex]\rho[/tex][tex]\delta[/tex]2uv/[tex]\delta[/tex]t2 + EI[tex]\delta[/tex]4uv/[tex]\delta[/tex]x4 = Lu + Lv. Does this mean it's linear or is there more to do.
     
  2. jcsd
  3. Mar 20, 2010 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Re: Linearity

    That is enough.
     
  4. Mar 20, 2010 #3
    Re: Linearity

    Cheers.
    What about this one then.
    ut - [tex]\alpha^2[/tex][tex]\nabla^2[/tex]u = ru(M -u) where [tex]\alpha[/tex], r & M are constants.

    ut - [tex]\alpha^2[/tex][tex]\nabla^2[/tex]u - ru(M -u) = 0
    L(u+v+w) = ut(u+v+w) + [tex]\alpha^2[/tex][tex]\nabla^2[/tex]u(u+v+w) - ru(M-u)(u+v+w) = utt + [tex]\alpha^2[/tex][tex]\nabla^2[/tex]u2 - ru2(M-u) + utv + [tex]\alpha^2[/tex][tex]\nabla^2[/tex]uv - ruv(M-u) + utw + [tex]\alpha^2[/tex][tex]\nabla^2[/tex]uw - ruw(M-u) = Lu + Lv + Lw
     
    Last edited: Mar 20, 2010
  5. Mar 20, 2010 #4
    Re: Linearity

    Are these equation linear or non-linear?

    ut + (1-u)ux = 0
    uxx + exutt = sin(x)
    uxx + uxy + uyy + ux = t2
     
  6. Mar 22, 2010 #5
    Re: Linearity

    Someone help please.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook