Svetlin G. Georgiev
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 .
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
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