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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Quasilinear evolution equations and parabolic systems

Author: Herbert Amann
Journal: Trans. Amer. Math. Soc. 293 (1986), 191-227
MSC: Primary 35K60; Secondary 34G20, 58D25
MathSciNet review: 814920
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Abstract: It is shown that general quasilinear parabolic systems possess unique maximal classical solutions for sufficiently smooth initial values, provided the boundary conditions are ``time-independent''. Moreover it is shown that, in the autonomous case, these equations generate local semiflows on appropriate Sobolev spaces. Our results apply, in particular, to the case of prescribed boundary values (Dirichlet boundary conditions).

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Additional Information

PII: S 0002-9947(1986)0814920-4
Keywords: Quasilinear parabolic systems, existence, regularity, flows, interpolation spaces
Article copyright: © Copyright 1986 American Mathematical Society