Blow up in finite time and dynamics of blow up solutions for the $L^2$–critical generalized KdV equation
نویسندگان
چکیده
منابع مشابه
Blow up in Finite Time and Dynamics of Blow up Solutions for the L–critical Generalized Kdv Equation
In this paper, we are interested in the phenomenon of blow up in finite time (or formation of singularity in finite time) of solutions of the critical generalized KdV equation. Few results are known in the context of partial differential equations with a Hamiltonian structure. For the semilinear wave equation, or more generally for hyperbolic systems, the finite speed of propagation allows one ...
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From these conservation laws, H appears as an energy space, so that it is a natural space in which to study the solutions. Note that p = 2 is a special case for equation (2). Indeed, from the integrability theory (see Lax [14]), we have for suitable u0 (u0 and its derivatives with fast decay at infinity) an infinite number of conservation laws. The general question is to understand the dynamics...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2002
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-02-00392-2