Delayed singularity formation for solutions of nonlinear partial differential equations in higher dimensions
AUTOR(ES)
John, Fritz
RESUMO
Strict solutions u of genuinely nonlinear homogeneous hyperbolic equations in two independent variables with initial data f(x) of compact support become singular after a time interval of order ∥f∥-1. In higher dimensions solutions initially of compact support are likely to have life expectancies of orders ∥f∥-2+ε at least. This is proved for the special case of solutions u(x1,..., xn, t) of a second order equation utt = Σi,jaijuxixj, where n ≥ 3 and where the coefficients aij are C∞-functions in the first derivatives of u, forming a symmetric positive definite matrix.
ACESSO AO ARTIGO
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=335889Documentos Relacionados
- ON ENTIRE SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS*
- Blow-up of solutions of nonlinear wave equations in three space dimensions
- Lower bounds for the life-span of solutions of nonlinear wave equations in three dimensions
- A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS*
- A STURM-LIOUVILLE THEOREM FOR NONLINEAR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS*