Global solutions to some nonlinear dissipative mildly degenerate Kirchhoff equations.
Global solvability for the degenerate Kirchhoff equation
Global solvability of a mixed problem for a nonlinear hyperbolic-parabolic equation in noncylindrical domains.
Global sovability for the degenerate Krichhoff equation with real anlytic data.
Hyperbolic equations with non-Lipschitz coefficients.
Hyperbolic parabolic equations with nonlinearity of Kirchhoff-Carrier type.
Intégrabilité d'une classe de systèmes de lois de conservation.
Minimal surfaces in pseudohermitian geometry
We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation...
New unilateral problems in stratigraphy
This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differential inclusions of degenerated hyperbolic-parabolic type , where H is the maximal monotonous graph of the Heaviside function and E is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the weather-limited rate constraint in the conservation...
Nonlocal and initial problems for quasilinear nonstrictly hyperbolic equations with general solutions represented by superpositions of arbitrary functions.
Oblique derivative problems for generalized Rassias equations of mixed type with several characteristic boundaries.
Oblique derivative problems for second-order hyperbolic equations with degenerate curve.
On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient.
On a weakly hyperbolic quasilinear mixed problem of second order
On an ODE Relevant for the General Theory of the Hyperbolic Cauchy Problem
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.
On global real analytic solutions of the degenerate Kirchhoff equation
On measure solutions to the zero-pressure gas model and their uniqueness
On measure solutions to the Zero-pressure gas model and their uniqueness
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