Existence and non‐existence of global solutions of a non‐local wave equation
Copyright policy )Existence and non‐existence of global solutions of a non‐local wave equation
AbstractWe 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 they blow up in finite time if p>1. We also present the growth rate at blow‐up. Copyright © 2004 John Wiley & Sons, Ltd.
- University of Louisiana at Lafayette United States
blow up, Asymptotic behavior of solutions to PDEs, Initial value problems for second-order hyperbolic equations, Mellin transforms, Second-order nonlinear hyperbolic equations
blow up, Asymptotic behavior of solutions to PDEs, Initial value problems for second-order hyperbolic equations, Mellin transforms, Second-order nonlinear hyperbolic equations
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