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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

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    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.
     
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