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2000 Mathematics Subject Classification: 34E20, 35L80, 35L15.In this paper we study an ODE in the complex plane. This is a key step in the search of new necessary conditions for the well posedness of the Cauchy Problem for hyperbolic operators with double characteristics.

On exact solutions of a degenerate quasilinear wave equation with source term.

Amroun, Nour-Eddine, Benaissa, Abbes (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

On global real analytic solutions of the degenerate Kirchhoff equation

Kunihiko Kajitani, Kaoru Yamaguti (1994)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On measure solutions to the zero-pressure gas model and their uniqueness

Li, Jiequan, Warnecke, Gerald (2002)

Proceedings of Equadiff 10

On measure solutions to the Zero-pressure gas model and their uniqueness

Jiequan Li, Gerald G. Warnecke (2002)

Mathematica Bohemica

The system of zero-pressure gas dynamics conservation laws describes the dynamics of free particles sticking under collision while mass and momentum are conserved. The existence of such solutions was established some time ago. Here we report a uniqueness result that uses the Oleinik entropy condition and a cohesion condition. Both of these conditions are automatically satisfied by solutions obtained in previous existence results. Important tools in the proof of uniqueness are regularizations, generalized...

On pseudosymmetric systems with one space variable

Tatsuo Nishitani, Sergio Spagnolo (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On second order nonlinear equations with rectilinear characteristics.

Gvazava, J. (2000)

Georgian Mathematical Journal

On some multidimensional versions of a characteristic problem for second-order degenerating hyperbolic equations.

Kharibegashvili, S. (1998)

Georgian Mathematical Journal

On some variational inequalities for nonclassical type operators

Sergey Glazatov (1992)

Banach Center Publications

The purpose of this paper is to make a brief review of results obtained in the theory of variational inequalities for nonclassical operators, namely, of degenerate hyperbolic and variable type.

On the Dirichlet problem in a characteristic rectangle for fourth order linear singular hyperbolic equations.

Kiguradze, T. (1999)

Georgian Mathematical Journal

On the existence of solutions for some nondegenerate nonlinear wave equations of Kirchhoff type

Jong Yeoul Park, Jeong Ja Bae (2002)

Czechoslovak Mathematical Journal

Let $Ω$ be a bounded domain in $ℝ^{n}$ with a smooth boundary $Γ$ . In this work we study the existence of solutions for the following boundary value problem: $\frac{\partial^{2} y}{\partial t^{2}} - M (\int_{Ω} {| \nabla y |}^{2} d x) Δ y - \frac{\partial}{\partial t} Δ y = f (y) in Q = Ω \times (0, \infty), . 1 y = 0 in Σ_{1} = Γ_{1} \times (0, \infty), M (\int_{Ω} {| \nabla y |}^{2} d x) \frac{\partial y}{\partial ν} + \frac{\partial}{\partial t} (\frac{\partial y}{\partial ν}) = g in Σ_{0} = Γ_{0} \times (0, \infty), y (0) = y_{0}, \frac{\partial y}{\partial t} (0) = y_{1} in Ω, (1)$ where $M$ is a $C^{1}$ -function such that $M (λ) \geq λ_{0} > 0$ for every $λ \geq 0$ and $f (y) = {| y |}^{α} y$ for $α \geq 0$ .