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Linearity math problem

  • Thread starter squenshl
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  • #1
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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.
 

Answers and Replies

  • #2
arildno
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That is enough.
 
  • #3
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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:
  • #4
479
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Are these equation linear or non-linear?

ut + (1-u)ux = 0
uxx + exutt = sin(x)
uxx + uxy + uyy + ux = t2
 
  • #5
479
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Someone help please.
 

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