Premium
Biow‐up of solutions of some nonlinear hyperbolic equations
Author(s) -
Kato Tosio
Publication year - 1980
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160330403
Subject(s) - mathematics , hyperbolic partial differential equation , nonlinear system , partial differential equation , mathematical analysis , elliptic partial differential equation , order (exchange) , physics , quantum mechanics , finance , economics
We prove that any nontrivial solution of certain nonlinear hyperbolic partial differential equations of second order blows up in a finite time if the initial data are localized, the initial velocity being on the average non‐negative.