Wasserstein kernels for one-dimensional diffusion problems |
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Authors: | Adrian Tudorascu |
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Affiliation: | School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States |
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Abstract: | We treat the evolution as a gradient flow with respect to the Wasserstein distance on a special manifold and construct the weak solution for the initial-value problem by using a time-discretized implicit scheme. The concept of Wasserstein kernel associated with one-dimensional diffusion problems with Neumann boundary conditions is introduced. On the basis of this, features of the initial data are shown to propagate to the weak solution at almost all time levels, whereas, in a case of interest, these features even help with obtaining the weak solution. Numerical simulations support our theoretical results. |
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Keywords: | 35B40 35D05 35D10 35K55 35K60 49M25 |
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