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On the existence or absence of global solutions for the multidimensional version of the second Darboux problem for some nonlinear hyperbolic equations

On the existence or absence of global solutions for the multidimensional version of the second... ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 3, pp. 402–416.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c S.S. Kharibegashvili, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 3, pp. 388–401. PARTIAL DIFFERENTIAL EQUATIONS On the Existence or Absence of Global Solutions for the Multidimensional Version of the Second Darboux Problem for Some Nonlinear Hyperbolic Equations S. S. Kharibegashvili Mathematical Institute, Georgian Academy of Sciences, Tbilisi, Georgia Received August 25, 2005 DOI: 10.1134/S001226610703010X 1. STATEMENT OF THE PROBLEM Consider the nonlinear wave equation of the form ∂ u Lu := − Δu + mu = f (u)+ F, (1) ∂t where f and F are given real functions, f is nonlinear, and u is the unknown real function; 2 2 m =const ≥ 0, Δ = ∂ /∂x ,and n ≥ 2. i=1 i n+1 Let D be a conical domain in the space R of the variables x =(x ,... ,x )and t; i.e., if D 1 n contains a point (x, t), then it contains the entire ray :(τx, τ t), 0 <τ < ∞.By S we denote the cone ∂D. We assume that the domain D is homeomorphic to the conical http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On the existence or absence of global solutions for the multidimensional version of the second Darboux problem for some nonlinear hyperbolic equations

Kharibegashvili, S.
Differential Equations , Volume 43 (3) – Apr 19, 2007
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References (22)

Publisher
Springer Journals
Copyright
Copyright © 2007 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S001226610703010X
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 3, pp. 402–416.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c S.S. Kharibegashvili, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 3, pp. 388–401. PARTIAL DIFFERENTIAL EQUATIONS On the Existence or Absence of Global Solutions for the Multidimensional Version of the Second Darboux Problem for Some Nonlinear Hyperbolic Equations S. S. Kharibegashvili Mathematical Institute, Georgian Academy of Sciences, Tbilisi, Georgia Received August 25, 2005 DOI: 10.1134/S001226610703010X 1. STATEMENT OF THE PROBLEM Consider the nonlinear wave equation of the form ∂ u Lu := − Δu + mu = f (u)+ F, (1) ∂t where f and F are given real functions, f is nonlinear, and u is the unknown real function; 2 2 m =const ≥ 0, Δ = ∂ /∂x ,and n ≥ 2. i=1 i n+1 Let D be a conical domain in the space R of the variables x =(x ,... ,x )and t; i.e., if D 1 n contains a point (x, t), then it contains the entire ray :(τx, τ t), 0 <τ < ∞.By S we denote the cone ∂D. We assume that the domain D is homeomorphic to the conical

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Differential Equations – Springer Journals

Published: Apr 19, 2007

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