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Global existence in the future and boundedness of submanifolds of solutions of a scalar comparison equation

✍ Scribed by Giancarlo Cantarelli

Book ID: 112908284
Publisher: Springer Milan
Year: 1995
Tongue: Italian
Weight: 473 KB
Volume: 44
Category: Article
ISSN: 0009-725X
DOI: 10.1007/bf02844677

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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 φ(__x__)⩾0 and $ \int \nolimits^{\infty} \_ {-\infty} \varphi (x) \, {\rm{d}}x\,= 1$. We show that solutions exist globally for 0<__p__⩽1, while