The Fuchsian Cauchy problem.
The function classes and global linear Goursat problems
The general method for solving of the boundary problems for the partial differential equations of any order II
The general method for solving the partial differential equation of any order with unknown function depending on any number of arguments and the system of such equations
The geometry of the space of Cauchy data of nonlinear PDEs
First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given in many equivalent ways - for instance, by means of Grassmann bundles. In this paper we generalize it by means of flag bundles, and develop the corresponding theory for higher-oder and infinite-order jet bundles. We show that this is a natural geometric framework...
The homogeneous balance of undetermined coefficients method and its application
The homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers. The proposed method can also be used to derive more general bilinear equation of nonlinear PDEs. The Eckhaus equation, the KdV equation and the generalized Boussinesq equation are chosen to illustrate the validity of our method. The proposed method is also a standard and computable method, which can...
The homogeneous Dirichlet problem for non-elliptic partial differential equations with strong nonlinearities
The Laplace method of the linear partial differential equations of the -th order
The Lie-algebraic discrete approximation scheme for evolution equations with Dirichlet/Neumann data.
The Riemann method for equations with leading partial derivative in .
The Semilinear Second-Order Hyperbolic Equation with Data Strongly Singular at One Point.
The solution of an axially symmetric boundary value problem of the generalized heat equation and its application in the technology of microschemes
The solution of embedding problems in the framework of GAPs with applications on nonlinear PDEs.
The solution operator for a partial differential equation with delay
Viene dimostrata l’esistenza e l’unicità globale della soluzione di un’equazione funzionale in uno spazio di Hilbert e si caratterizza il generatore infinitesimale del semigruppo ad essa associato. Il risultato è applicato ad equazioni integrodifferenziali a derivate parziali di tipo parabolico in cui compaiono argomenti con ritardo (discreto e continuo) nelle derivate spaziali di ordine massimo.
Théorème de Cauchy-Kovalevsky et théorème d'unicité d'Holmgren pour des fonctions analytiques d'une infinité de variables
Théorème d'indice et régularité pour une classe d'opérateurs elliptiques et dégénérés
Théorème d'indice et régularité pour une classe d'opérateurs elliptiques et dégénérés
Théorie de la diffusion pour des équations semi linéaires
Time deformations of powers of the wave operator.
Time discretization of parabolic problems by the discontinuous Galerkin method