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Cauchy Problem with Subcritical Nonlinearity

✍ Scribed by Jan W Cholewa; Tomasz Dlotko

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
250 KB
Volume
210
Category
Article
ISSN
0022-247X

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✦ Synopsis

The semilinear parabolic system on R n with subcritical nonlinearity is studied as p Ž n . an abstract evolutionary equation in a Banach space X [ L L R . As in the case of bounded domains the existence of a strongly continuous semigroup of global X ␣ -solutions and its dissipativeness is shown to follow from a single estimate of solutions. Despite the lack of compactness of the Sobolev embeddings in R n the compactness of trajectories of the semigroup is proved using the auxiliary estimate p Ž n Ž < < 2 . . of solutions in a weighted space L L R , 1 q x , and the existence of a global attractor is also shown. Thus this paper generalizes earlier considerations and provides a basis for further applications.

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