Hokkaido Mathematical Journal

The lifespan of solutions to wave equations with weighted nonlinear terms in one space dimension

Kyouhei WAKASA

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Abstract

In this paper, we consider the initial value problem for nonlinear wave equation with weighted nonlinear terms in one space dimension. Kubo & Osaka & Yazici [4] studied global solvability of the problem under different conditions on the nonlinearity and initial data, together with an upper bound of the lifespan for the problem. The aim of this paper is to improve the upper bound of the lifespan and to derive its lower bound which shows the optimality of our new upper bound.

Article information

Source
Hokkaido Math. J., Volume 46, Number 2 (2017), 257-276.

Dates
First available in Project Euclid: 30 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1498788020

Digital Object Identifier
doi:10.14492/hokmj/1498788020

Mathematical Reviews number (MathSciNet)
MR3677883

Zentralblatt MATH identifier
06754735

Subjects
Primary: 35L71: Semilinear second-order hyperbolic equations 35E15: Initial value problems
Secondary: 35A01: Existence problems: global existence, local existence, non-existence 35A09: Classical solutions 35B44: Blow-up

Keywords
nonlinear wave equation lifespan one space dimension

Citation

WAKASA, Kyouhei. The lifespan of solutions to wave equations with weighted nonlinear terms in one space dimension. Hokkaido Math. J. 46 (2017), no. 2, 257--276. doi:10.14492/hokmj/1498788020. https://projecteuclid.org/euclid.hokmj/1498788020


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