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Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow

✍ Scribed by Gianluca Crippa, Magali Lécureux-Mercier

Book ID
120780765
Publisher
SP Birkhäuser Verlag Basel
Year
2012
Tongue
English
Weight
279 KB
Volume
20
Category
Article
ISSN
1021-9722

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Existence and non-existence of global so
Existence and non-existence of global solutions of a non-local wave equation
✍ Azmy S. Ackleh; Keng Deng 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 87 KB 👁 1 views

## 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