The Cauchy problem for semilinear hyperbolic equation with characteristic degeneration on the initial hyperplane

The Cauchy problem for semilinear hyperbolic equation with characteristic degeneration on the... In this paper, we study the well posed‐ness of Cauchy problem for a class of hyperbolic equation with characteristic degeneration on the initial hyperplane. By a delicate analysis of two integral operators in terms of Bessel functions, we give the uniform weighted estimates of solutions to the linear problem with a parameter m∈(0,1) and establish local and global existences of solution to the semilinear equation. Meanwhile, we derive the existence of solutions to semilinear generalized Euler‐Poisson‐Darboux equation with a negative parameter α∈(−1,0). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Methods in the Applied Sciences Wiley

The Cauchy problem for semilinear hyperbolic equation with characteristic degeneration on the initial hyperplane

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2018 John Wiley & Sons, Ltd.
ISSN
0170-4214
eISSN
1099-1476
D.O.I.
10.1002/mma.4750
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study the well posed‐ness of Cauchy problem for a class of hyperbolic equation with characteristic degeneration on the initial hyperplane. By a delicate analysis of two integral operators in terms of Bessel functions, we give the uniform weighted estimates of solutions to the linear problem with a parameter m∈(0,1) and establish local and global existences of solution to the semilinear equation. Meanwhile, we derive the existence of solutions to semilinear generalized Euler‐Poisson‐Darboux equation with a negative parameter α∈(−1,0).

Journal

Mathematical Methods in the Applied SciencesWiley

Published: Jan 1, 2018

Keywords: ; ; ;

References

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