Laplace Transform Method for Parabolic Problems with Time-Dependent Coefficients

@article{Lee2013LaplaceTM,
  title={Laplace Transform Method for Parabolic Problems with Time-Dependent Coefficients},
  author={Hyoseop Lee and Jinwoo Brian Lee and Dongwoo Sheen},
  journal={SIAM J. Numer. Anal.},
  year={2013},
  volume={51},
  pages={112-125}
}
The Laplace transform method has proven to be very efficient for dealing with parabolic problems whose coefficients are time independent, and it is easily parallelizable. However, the method has not been proven to be applicable to linear problems whose coefficients are time dependent. The reason is that the Laplace transform of two time-dependent functions leads to a convolution of the Laplace transformed functions in the dual variable. In this paper, we propose a Laplace transform method to… 
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