Asymptotically Short Term Behavior of Solutions to One Dimensional Diffusion Processes

@article{Allen1999AsymptoticallyST,
  title={Asymptotically Short Term Behavior of Solutions to One Dimensional Diffusion Processes},
  author={G. Donald Allen and Sayed R. El Attar and Jeff Morgan},
  journal={Journal of Mathematical Analysis and Applications},
  year={1999},
  volume={240},
  pages={145-162}
}
Consider the problem of solving the diffusion equation ­ u s p x u , 0 x p , t ) 0, Ž . Ž . t x ­ x u 0, t s u p , t s 0, t ) 0, Ž . Ž . 1 Ž . u x , 0 s u x , Ž . Ž . 0 Ž . w x 1ŽŽ . . where p x is a smooth, positive function on 0, p and u g L 0, p , R . 0 If we define the operator A: D A a L 0, p , R Ž . Ž . Ž . via d A w s p x w Ž . Ž . Ž . x dx for all w g D A s W 2, 1 0, p , R l W 1, 1 0, p , R , Ž . Ž . Ž . Ž . Ž . 0 

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