Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Existence and nonexistence of global solutions of the wave equation with a nonlinear boundary condition

Authors: Azmy S. Ackleh and Keng Deng
Journal: Quart. Appl. Math. 59 (2001), 153-158
MSC: Primary 35L05; Secondary 35B40, 35L15, 35L20
DOI: https://doi.org/10.1090/qam/1811100
MathSciNet review: MR1811100
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Abstract: We study the initial-boundary value problem

$\displaystyle {u_{tt}} = {u_{xx}}, \qquad 0 < x < \infty , \qquad t > 0,$

$\displaystyle - {u_x}\left( 0, t \right) = h\left( u\left( 0, t \right) \right), \qquad t > 0,$

$\displaystyle u\left( x, 0 \right) = f\left( x \right), \qquad {u_t}\left( x, 0 \right) = g\left( x \right), \qquad 0 < x < \infty .$

We establish criteria for existence and nonexistence of global solutions, and we present the growth rate at blow-up.

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DOI: https://doi.org/10.1090/qam/1811100
Article copyright: © Copyright 2001 American Mathematical Society

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