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Optimal bounds in reaction diffusion problems with variable diffusion coefficient

by R. Sperb

(Report number 2008-32)

Abstract
A diffussion-reaction problem is considered involving a variable diffusion coefficient. A maximum principle for a functional of the solution is proven, which allows to derive bounds for various quantities of interest. The bounds are optimal in the sense that they become sharp if the domain is a slab or an $N$-sphere and the diffusion coefficient has an appropriate form.

Keywords:

@Techreport{S08_393,
  author = {R. Sperb},
  title = {Optimal bounds in reaction diffusion problems with variable diffusion coefficient},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2008-32},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2008/2008-32.pdf },
  year = {2008}
}

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