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Consider the partial differential equation $\quad$ $ u_{tt}+u_{xxxx} + \cos x \cos u = 0$.

Which of the following statements is correct?

  • Let $ L u = u_{tt}+u_{xxxx} + \cos x \cos u $. So, the PDE can be written as $ L u = 0 $ and therefore, it is homogeneous.

  • Let $ L u = u_{tt}+u_{xxxx} $. So, the PDE can be written as $ L u = - \cos x \cos u $ and therefore, it is not homogeneous.

I think the second one is the right one. Could you explain a little?

Also the partial differential equation is semilinear and therefore it is also quasi-linear. Is this correct?

Jacob S.
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  • https://math.stackexchange.com/questions/597962/how-to-decide-whether-pde-is-homogeneous-or-non-homogeneous – ℋolo Mar 11 '18 at 01:57
  • for the second part: https://math.stackexchange.com/questions/1839532/difference-between-second-order-quasi-linear-and-semi-linear-pde – ℋolo Mar 11 '18 at 02:12
  • $\cos u$ is not a linear operator – Dylan Mar 11 '18 at 16:33

0 Answers0