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Almost global existence of solutions of quasi-linear hyperbolic equations

โœ Scribed by Albert J. Milani; B. Brosowski

Publisher
John Wiley and Sons
Year
1989
Tongue
English
Weight
239 KB
Volume
11
Category
Article
ISSN
0170-4214

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## Abstract We study the initial value problem where $ \|u(\cdot,t)\| = \int \nolimits ^ {\infty} \_ {- \infty}\varphi(x) | u( x,t ) | {\rm{ d }} x$ with ฯ†(__x__)โฉพ0 and $ \int \nolimits^{\infty} \_ {-\infty} \varphi (x) \, {\rm{d}}x\,= 1$. We show that solutions exist globally for 0<__p__โฉฝ1, while