Conditional stability up to the final time for backward-parabolic equations with Log-Lipschitz coefficients

Abstract

We prove logarithmic conditional stability up to the final time for backward-parabolic operators whose coefficients are Log-Lipschitz continuous in $t$ and Lipschitz continuous in $x$. The result complements previous achievements of Del Santo and Prizzi (2009) and Del Santo, Jaeh and Prizzi (2015), concerning conditional stability (of a type intermediate between Hoelder and logarithmic), arbitrarily closed, but not up to the final time.

35 pages. Accepted manuscript. arXiv admin note: text overlap with arXiv:1407.4616

References in corpus (1)

• Conditional stability for backward parabolic operators with Osgood continuous coefficients

Cited by in corpus (1)

• Reconstruction of the initial condition in parabolic equations with Log-Lipschitz coefficients