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Certain nonlocal problem for a degenerate hyperbolic equation
Mathematical Notes, 1992The equation \((*)\) \(| y|^ m u_{xx}- u_{yy}=0\), \(m>0\) is considered in a domain bounded by characteristics of \((*)\). Values of integrals of \(u\) along characteristics are given. The author proves uniqueness and existence of the solution to the problem mentioned above.
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Local solution for a degenerate hyperbolic equation with memory
Nonlinear Analysis: Theory, Methods & Applications, 1994In this paper, the local solvability in suitable Sobolev-type spaces for the nonlocal equation \[ u'' - m \bigl( (\Lambda u,u) \bigr) \cdot \Lambda u + \dot a* \biggl( m \bigl( (\Lambda u,u) \bigr) \cdot \Lambda u \biggr) = 0, \quad u(0) = u_0,\;u'(0) = u_1, \tag{*} \] is studied. Here \(m(r)\) is a nonnegative function (possibly vanishing somewhere), \
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On the nonlocal problem for a hyperbolic equation with a parabolic degeneration
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022Anna Valerevna Tarasenko +1 more
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Singular perturbation hyperbolic–parabolic for degenerate nonlinear equations of Kirchhoff type
Nonlinear Analysis: Theory, Methods & Applications, 2001Massimo Gobbino
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Cauchy problem for degenerate hyperbolic equations
Communications on Pure and Applied Mathematics, 1980openaire +2 more sources
The Cauchy problem for general quasilinear hyperbolic equations with degenerate rank 0
Complex Variables and Elliptic Equations, 2006Zuoliang Xu
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Large-time behavior of solutions to degenerate damped hyperbolic equations
Siberian Mathematical Journal, 2016N M Tri
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Boundary Value Problems for Degenerate Hyperbolic Systems of First Order Equations
Complex Variables and Elliptic Equations, 2002Guo Chun Wen
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On local solutions of some mildly degenerate hyperbolic equations
Nonlinear Analysis: Theory, Methods & Applications, 1993exaly