Degenerate parabolic equations

with initial data measures

Author:
Daniele Andreucci

Journal:
Trans. Amer. Math. Soc. **349** (1997), 3911-3923

MSC (1991):
Primary 35K65, 35R05; Secondary 35K55, 35K15

DOI:
https://doi.org/10.1090/S0002-9947-97-01530-4

MathSciNet review:
1333384

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Abstract | References | Similar Articles | Additional Information

Abstract: We address the problem of existence of solutions to degenerate (and nondegenerate) parabolic equations under optimal assumptions on the initial data, which are assumed to be measures. The requirements imposed on the initial data are connected both with the degeneracy of the principal part of the equation, and with the form of the nonlinear forcing term. The latter depends on the space gradient of a power of the solution. Applications to related problems are also outlined.

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Additional Information

**Daniele Andreucci**

Affiliation:
Università “La Sapienza”, Dipartimento di Metodi e Modelli Matematici, via A. Scarpa 16, 00161 Roma, Italy

Email:
andreucc@dmmm.uniroma1.it

DOI:
https://doi.org/10.1090/S0002-9947-97-01530-4

Received by editor(s):
August 15, 1994

Received by editor(s) in revised form:
March 20, 1995

Additional Notes:
The author is a member of GNFM of Italian CNR. Work supported by MURST project “Problemi non lineari...”

Article copyright:
© Copyright 1997
American Mathematical Society