Laser induced Photoacoustic simulation

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After the approximation that neglects thermal diffusion, the problem just consists of the decoupled pressure equation. That is what needs to be solved, right? The exact solution seems to have been calculated for a sinusoidal heat source (decaying in x), after which Fourier transformation was used to calculate it for the Gaussian source. But, if I understand correctly, you need a numerical solution? Also, is there only one space variable x? Please let me know. It seems to be a pretty interesting and tractable problem.

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