From conservative to dissipative systems through quadratic change of time, with application to the curve-shortening flow (Q1702099)

The purpose of this paper is to study dissipative systems, e.g. the heat equation, which can be simply obtained from conservative ones. First dissipative systems on a \(d\)-dimensional torus are defined in the sense of distributions. The first theorem states that the set of dissipative solutions is convex and compact for a certain topology. The second theorem has a more technical character. The proofs use Cauchy-Schwarz inequality.