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

Zhang Kangqun | Zendy

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

Author(s) -

Zhang Kangqun

Publication year - 2018

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4750

Subject(s) - mathematics , hyperplane , bessel function , mathematical analysis , initial value problem , cauchy problem , hyperbolic partial differential equation , heat equation , cauchy distribution , partial differential equation , geometry

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).

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