Symmetry of the barochronous motions of a gas.
Symmetry operators for the Fokker-Planck-Kolmogorov equation with nonlocal quadratic nonlinearity.
Symmetry operators of a Hartree-type equation with quadratic potential.
Symmetry properties for the extremals of the Sobolev trace embedding
Symmetry results for viscosity solutions of fully nonlinear uniformly elliptic equations
We study uniformly elliptic fully nonlinear equations , and prove results of Gidas–Ni–Nirenberg type for positive viscosity solutions of such equations. We show that symmetries of the equation and the domain are reflected by the solution, both in bounded and unbounded domains.
Systèmes hyperboliques à multiplicité constante
Systèmes mathématiques aux structures entremelées. Problèmes aux limites pour certains systèmes différentiels aux différences, ordinaires ou aux dérivées totales au sens de M. M. Picone
Systems of Clairaut type
A characterization of systems of first order differential equations with (classical) complete solutions is given. Systems with (classical) complete solutions that consist of hyperplanes are also characterized.
Systems of meromorphic microdifferential equations
We introduce the notion of system of meromorphic microdifferential equations. We use it to prove a desingularization theorem for systems of microdifferential equations.
Systems of multi-dimensional Laplace transforms and a heat equation.
Syzygies of modules and applications to propagation of regularity phenomena.
Propagation of regularity is considered for solutions of rectangular systems of infinite order partial differential equations (resp. convolution equations) in spaces of hyperfunctions (resp. C∞ functions and distributions). Known resulys of this kind are recovered as particular cases, when finite order partial differential equations are considered.
Temps de vie et comportement explosif des solutions d'équations d'ondes quasi-linéaires en dimension deux
Teoria dei fasci e trasformazioni integrali per -moduli tra varietà di Grassmann
The Asymptotics of the Heat Equation for a Boundary Value Problem.
The Bernoulli manifolds for nonelliptic quasilinear systems of first order and applications in continuum mechanics
The blow-up curve of solutions of mixed problems for semilinear wave equations with exponential nonlinearities in one space dimension, II
The Carleman formula for the Helmholtz equation on the plane.
The Cauchy problem for hyperbolic systems with Hölder continuous coefficients with respect to the time variable
We discuss the local existence and uniqueness of solutions of certain nonstrictly hyperbolic systems, with Hölder continuous coefficients with respect to time variable. We reduce the nonstrictly hyperbolic systems to the parabolic ones and by use of the Tanabe-Sobolevski’s method and the Banach scale method we construct a semi-group which gives a representation of the solution to the Cauchy problem.
The Cauchy problem for systems through the normal form of systems and theory of weighted determinant
The author propose what is the principal part of linear systems of partial differential equations in the Cauchy problem through the normal form of systems in the meromorphic formal symbol class and the theory of weighted determinant. As applications, he choose the necessary and sufficient conditions for the analytic well-posedness ( Cauchy-Kowalevskaya theorem ) and well-posedness (Levi condition).
The Cauchy problem for the two dimensional Euler–Poisson system
The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In the 3D case Guo [7] first constructed a global smooth irrotational solution by using the dispersive Klein-Gordon effect. It has been conjectured that same results should hold in the two-dimensional case. In our recent work [13], we proved the existence of a family of smooth solutions by constructing the wave operators for the 2D system....