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....
The Cauchy problem with logarithmic ramifications for -modules
The change in electric potential due to lightning
The change in the electric potential due to lightning is evaluated. The potential along the lightning channel is a constant which is the projection of the pre-flash potential along a piecewise harmonic eigenfunction which is constant along the lightning channel. The change in the potential outside the lightning channel is a harmonic function whose boundary conditions are expressed in terms of the pre-flash potential and the post-flash potential along the lightning channel. The expression for the...
The complex reflection method for some classes of equations with the third derivative distinguished.
The Convergence of Successive Approximations for Boundary Value Problems of Hyperbolic Equations in the Banach Space
The current situation in the linear problem of Molodenskii
Si prova l'esistenza di un'unica soluzione debole che dipende con continuità dai dati al contorno per il problema lineare di Molodenskii in approssimazione quasi sferica, nel caso che la superficie al contorno soddisfi una condizione di cono. Si segue un approccio costruttivo diretto, che generalizza una procedura precedentemente elaborata per il problema semplice di Molodenskii. Inoltre si prova che la soluzione ha derivate prime a quadrato integrabile al contorno, il che è essenziale per le applicazioni...
The decomposition method for linear, one-dimensional, time-dependent partial differential equations.
The differential form method for finding symmetries.
The Dirichlet boundary conditions and related natural boundary conditions in strengthened Sobolev spaces for discretized parabolic problems.
The Dirichlet problem and weighted spaces. II.
The dynamics of a tied body against an obstacle
The Ekeland's variational principle for vector-valued multifunctions.