Non-uniform dependence and well-posedness for the hyperelastic rod equation

It is shown that the solution map for the hyperelastic rod equation is not uniformly continuous on bounded sets of Sobolev spaces with exponent greater than 3/2 in the periodic case and greater than 1 in the non-periodic case. The proof is based on the method of approximate solutions and well-posedness estimates for the solution and its lifespan. (C) 2010 Elsevier Inc. All rights reserved.