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Oblique derivative problems for second order nonlinear equations of mixed type with degenerate hyperbolic curve

Acta Mathematica Sinica, English Series, 2011
The present paper deals with oblique derivative problems for second order nonlinear equations of mixed type with degenerate hyperbolic curve, which include the Tricomi problem as a special case.
Guo Chun Wen
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Boundary Value Problems for Quasi-Hyperbolic Equations with Degeneration

Mathematical Notes, 2022
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Kozhanov, A. I., Spiridonova, N. R.
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A kinetic approach to comparison properties for degenerate parabolic–hyperbolic equations with boundary conditions

Journal of Differential Equations, 2006
We study the comparison principle for degenerate parabolic–hyperbolic equations with initial and nonhomogeneous boundary conditions. We prove a comparison theorem for any entropy sub- and supersolution.
Kobayasi, Kazuo
exaly   +2 more sources

Local solutions for a nonlinear degenerate Hyperbolic equation

Nonlinear Analysis: Theory, Methods & Applications, 1986
The author investigates local solutions for the initial-boundary value problem associated to the nonlinear degenerated hyperbolic equation of the type \(u_{tt}-M(\int_{\Omega}| \nabla u|^ 2dx)\Delta u=0,\) which comes from the mathematical description of the vibrations of an elastic stretched string.
Ebihara, Y., Medeiros, L. A., Milla Miranda, M.   +2 more
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Weakly Degenerate Hyperbolic Equations

Differential Equations, 2003
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A nonlocal problem for degenerate hyperbolic equation

Russian Mathematics, 2017
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Repin, O. A., Kumykova, S. K.
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Hyperbolic Phenomena in a Degenerate Parabolic Equation

Journal of Partial Differential Equations, 1997
The author studies an equation of the form \[ u_t = (\phi (u)\psi (u_x))_x, \quad (x,t)\in\mathbb{R}\times (0,\infty), \] where \(\phi : \mathbb{R}^+\mapsto \mathbb{R}^+\) is smooth, \(\phi\in C[0,+\infty)\), \(\phi(0)=0\), \(\phi'(s)>0\;(s>0)\), \(\lim_{s\to +0}s/\phi (s) =0\), and \(\psi :\mathbb{R}\mapsto \mathbb{R}\) is a strictly increasing smooth
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The Dirichlet Problem for a Degenerate Hyperbolic Equation in a Rectangle

Differential Equations, 2001
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Nonhomogeneous Dirichlet Problems for Degenerate Parabolic-Hyperbolic Equations

Archive for Rational Mechanics and Analysis, 2002
This paper is dedicated to study initial boundary value problem for the parabolic-hyperbolic equation \[ \partial_t u - \Delta b(u) + \text{div} \Phi(u) = g(x,t), \] \[ u _{t=0} = u_0(x), \qquad u _{\partial \Omega \times (0,T)} = a_0(x), \] in the case of nonhomogeneous boundary data \(a_0\).
MASCIA, Corrado, Alessio Porretta, TERRACINA, Andrea   +2 more
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A degenerate hyperbolic equation under Levi conditions

ANNALI DELL'UNIVERSITA' DI FERRARA, 2006
In the present study the author deals with the second-order equations of the form \[ \Biggl(D^2_t- \sum^n_{i,j=1} a_{ij}(t, x)D_{x_i} D_{x_j}+ \sum^n_{j=1} b_j(t, x)D_{x_j}+ C(t, x)\Biggr) u(t, x)= 0,\tag{1} \] where \(t\in [0,T]\), \(x\in\mathbb{R}^n\), \(D= {1\over i}\partial\), with \[ a(t,x,\xi):= \sum^n_{i,j=1} a_{ij}(t, x)\xi_i\xi_j\geq 0,\quad t\
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