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Convergence of the strongly damped nonlinear Klein-Gordon equation in ℝn with radial symmetry

Published online by Cambridge University Press:  14 November 2011

Joel D. Avrin
Joel D. Avrin
Affiliation:
University of North Carolina at Charlotte, Charlotte, North Carolina 28223, U.S.A.
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Synopsis

We consider the strongly-damped Klein–Gordon equation in ℝ3 in the case where the initial data possess radial symmetry. With the latter assumption we are able to extend the result of [2] which assumed a bounded spatial domain. Specifically, we construct a global weak solution v of theundamped equation for high powers p which can be approximated arbitrarily closely (for small α) by the global strong solutions of the damped equation found by Aviles and Sandefur [1].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 1-2 , 1987 , pp. 169 - 174
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Aviles, P. and Sandefur, J.. Nonlinear second order equations with applications to partial differential equations. J. Differential Equations 58 (1985), 404–427.Google Scholar
2Avrin, J.. Convergence properties of the nonlinear Klein-Gordon equation. J. Differential Equations 67 (1987), 243–255.Google Scholar
3Engler, H.. Existence of radially symmetric solutions of strongly-damped wave equations (to appear).Google Scholar
4Ginebre, J. and Velo, G.. The global Cauchy problem for the non linear Klein-Gordon equation. Math. Z. 189 (1985), 487–505.CrossRefGoogle Scholar
5Reed, M.. Abstract Non-Linear Wave Equations (Berlin: Springer, 1976).Google Scholar
6Strauss, W. A.. Existence of solitary waves in higher dimensions. Comm. Math. Phys. 55 (1977), 149–162.CrossRefGoogle Scholar
7Strauss, W.. On weak solutions of semilinear hyperbolic equations. An. Acad. Brazil Cienc. 42 (1970), 645–651.Google Scholar