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I need to solve this:

$$ \begin{cases} U_{tt}= \Delta U + |x|^2 \sin t \\ U(x,0) = |x|^4 + |x|^2 \\ U_t(x,0) = |x|^4 - |x|^2 \end{cases} $$

in 3 dimensions $x = \{x_1, x_2, x_3\}$

  • 1
    Are you looking for solutions in $\mathbb{R}^3\times [0,\infty[$? In this case, perhaps you could use *superposition principle*, *Kirckhhoff formula* and *Duhamel principle* (see Evan's PDEs book, §§2.4.1.c & 2.4.2) to build a solution... But this way to the solution really requires a lot of work.2011-12-27
  • 0
    How to rewrite the PDE in terms of the dependent variable $U$ and the independent variables $x_1$ , $x_2$ and $x_3$ ?2012-10-24
  • 0
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