Svetlin G. Georgiev
Abstract:
We study the solutions to the the radial 2-dimensional wave equation
where
and
in
.
We show that this Cauchy problem, with values into a
hyperbolic space, is ill posed in subcritical Sobolev spaces.
In particular, we construct a function
in the space
,
with
,
,
, and
, for which the solution satisfies
.
In doing so, we provide a counterexample to estimates
in [1].
Submitted March 16, 2004. Published May 26, 2004.
Math Subject Classifications: 35L10, 35L50
Key Words: Wave equation, blow-up, hyperbolic space.
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Svetlin Georgiev Georgiev University of Sofia Faculty of Mathematics and Informatics Department of Differential Equations, Bulgaria email: sgg2000bg@yahoo.com |
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