Improved Kato’s lemma on ordinary differential inequality and its application to semilinear wave equations

By H. Takamura. 2014

60 citations recorded by the source corpus.

Abstract We are interested in the upper bound of the lifespan of solutions of semilinear wave equations. For the sub-critical case in high dimensions, it has been believed that the basic tools of its analysis are Kato’s lemma on ordinary differential inequalities and the rescaling argument in the functional method. But there is a small lack of delicate analysis and no published paper about this. Here we give a simple alternative proof by means of improved Kato’s lemma without any rescaling argument.

Subfields: Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/941029892f8facb7cc2175df795c6b67163e408a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. A. Palmieri
2. Wenhui Chen

In Mathematical Physics

1. Wenhui Chen
2. A. Palmieri
3. Ryo Ikehata

Citations in the corpus

• Nonexistence of global solutions for the semilinear Moore – Gibson – Thompson equation in the conservative case (2019, background): “(4) The lifespan of solutions to (3) that blow up in finite time has been intensively considered [26, 47, 48, 49, 27, 9, 41, 52, 40, 15].”