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Global Solution and Regularizing Properties on a Class of Nonlinear Evolution Equation

✍ Scribed by Jaime E Muñoz Rivera

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
853 KB
Volume
128
Category
Article
ISSN
0022-0396

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✦ Synopsis

In this paper we will consider the equation

where

The initial value problem is proved to be locally well posed for initial data taken in D(A 2 )_D(A 3Â2 ) and globally well posed for small data, in this case we also show the exponential decay of the solution as time goes to infinity. The main result of this paper is to prove that the solution has the smooting effect property on the initial data. This means that, if the initial data belongs to D(A 2 )_D(A 3Â2 ) then the solution u belongs to C (]0, + [; D(A k )) \k # N, provided M, N, and R are C -function.

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The results of this paper are contained in a doctoral thesis submitted to the Graduate School of Arts and Sciences of New York University. Reproduction in whole or in part is permitted for any purpose of the United States Government.