The behavior at infinity of a solution to a Sobolev type system.
The Cauchy problem and Hadamard's example
The Cauchy problem for operators with injective symbol in the Lebesgue space in a domain.
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 Dirichlet-Neumann operator on continuous functions
The evolution of the Dirac field in cuved space-times.
The Fuchsian Cauchy problem.
The Lie-algebraic discrete approximation scheme for evolution equations with Dirichlet/Neumann data.
The Riemann method for equations with leading partial derivative in .
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.
Time discretization of parabolic problems by the discontinuous Galerkin method