RT Journal Article
T1 On the Cauchy problem and initial traces for a degenerate parabolic equation
A1 Di Benedetto, E.
A1 Herrero, Miguel A.
AB The authors study the Cauchy problem for the degenerate parabolic equation ut = div(|Du| p−2 Du)(p<2), and find sufficient conditions on the initial trace u0 (and in particular on its behaviour as |x|→∞) for existence of a solution in some strip RN × (0,T). Using a Harnack type inequality they show that these conditions are optimal in the case of nonnegative solutions. Uniqueness of solutions is shown if u0 belongs to L1loc(RN), but is left open in the case that u0 is merely a locally bounded measure. The results are closely related to papers by Aronson-Caffarelli, Benilan-Crandall-Pierre, and Dahlberg-Kenig about the porous medium equation ut = Δum. The proofs are different and allow one to generalize some of the above results to equations with variable coefficients.
PB American Mathematical Society
SN 0002-9947
YR 1989
FD 1989-07
LK https://hdl.handle.net/20.500.14352/57767
UL https://hdl.handle.net/20.500.14352/57767
LA eng
NO NSF
NO CICYT
DS Docta Complutense
RD 6 abr 2025