| Full text | |
| Author(s): |
Figueira, Renata O.
;
Panthee, Mahendra
Total Authors: 2
|
| Document type: | Journal article |
| Source: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. N/A, p. 17-pg., 2023-04-23. |
| Abstract | |
In this work we consider the initial value problem (IVP) for the generalized Benjamin equation f partial differential tu - l9-l partial differential x2u - partial differential x3u + up partial differential xu = 0, x, t is an element of R, p >= 1, (1) u(x, 0) = u0(x), where u = u(x, t) is a real valued function, 0 < l < 1 and 9-l is the Hilbert transform. This model was introduced by Benjamin [3] and describes unidirectional propagation of long waves in a two-fluid system where the lower fluid with greater density is infinitely deep and the interface is subject to capillarity. We prove that the local solution to the IVP (1) for given data in the spaces of functions analytic on a strip around the real axis continue to be analytic without shrinking the width of the strip in time. We also study the evolution in time of the radius of spatial analyticity and show that it can decrease as the time advances. Finally, we present an algebraic lower bound on the possible rate of decrease in time of the uniform radius of spatial analyticity. (AU) | |
| FAPESP's process: | 21/04999-9 - Evolution of the radius of analyticity for dispersive equations and systems involving them |
| Grantee: | Renata de Oliveira Figueira |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 20/14833-8 - Nonlinear dispersive wave models |
| Grantee: | Mahendra Prasad Panthee |
| Support Opportunities: | Regular Research Grants |