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Quasilinear evolution equations and parabolic systems


Author: Herbert Amann
Journal: Trans. Amer. Math. Soc. 293 (1986), 191-227
MSC: Primary 35K60; Secondary 34G20, 58D25
DOI: https://doi.org/10.1090/S0002-9947-1986-0814920-4
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

DOI: https://doi.org/10.1090/S0002-9947-1986-0814920-4
Keywords: Quasilinear parabolic systems, existence, regularity, flows, interpolation spaces
Article copyright: © Copyright 1986 American Mathematical Society

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