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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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: 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

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