Energy solutions to one-dimensional singular parabolic problems with $BV$ data are viscosity solutions

Atsushi Nakayasu; Piotr Rybka

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arXiv · 1603.07502

Energy solutions to one-dimensional singular parabolic problems with $BV$ data are viscosity solutions

Atsushi Nakayasu·Piotr Rybka

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Abstract

We study one-dimensional very singular parabolic equations with periodic boundary conditions and initial data in $BV$, which is the energy space. We show existence of solutions in this energy space and then we prove that they are viscosity solutions in the sense of Giga-Giga.

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Atsushi Nakayasu, Piotr Rybka. 2016-03-24. Energy solutions to one-dimensional singular parabolic problems with $BV$ data are viscosity solutions. https://arxiv.org/abs/1603.07502

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