On analytic solutions to the generalized Cauchy problem with data on three surfaces for a quasilinear system.
On Asymptotic Behavior of Solution for the Navier-Stokes Equations in a Time Dependent Domain.
On blow-up of solution for Euler equations
We present numerical evidence for the blow-up of solution for the Euler equations. Our approximate solutions are Taylor polynomials in the time variable of an exact solution, and we believe that in terms of the exact solution, the blow-up will be rigorously proved.
On blow-up of solution for Euler equations
We present numerical evidence for the blow-up of solution for the Euler equations. Our approximate solutions are Taylor polynomials in the time variable of an exact solution, and we believe that in terms of the exact solution, the blow-up will be rigorously proved.
On Borel summable solutions of the multidimensional heat equation
We give a new characterisation of Borel summability of formal power series solutions to the n-dimensional heat equation in terms of holomorphic properties of the integral means of the Cauchy data. We also derive the Borel sum for the summable formal solutions.
On boundary integral equations of the first kind for the bi-laplacian in a polygonal plane domain
On closed-form solutions of some nonlinear partial differential equations.
On exact solutions of a degenerate quasilinear wave equation with source term.
On explicit and numerical solvability of parabolic initial-boundary value problems.
On generalized heat polynomials.
On Green's Function and Eigenvalues of Nonuniformly Elliptic Boundary Value Problems.
On hyperbolic partial differential equations in Banach spaces
Viene dimostrata l'esistenza di soluzioni del problema di Darboux per l'equazione iperbolica sul planiquarto , . Qui, è una funzione continua, con valori in uno spazio Banach che soddisfano alcune condizioni di regolarità espresse in termini della misura di non-compattezza .
On M. Kac's probabilistic formula for the solution of the telegraphist's equation
On Maximal Functions and Parabolic Limits.
On perturbative cubic nonlinear Schrödinger equations under complex nonhomogeneities and complex initial conditions.
On properties of nonlinear second-order systems under nonlinear impulse perturbations.
On quadrature methods for the double layer potential equation over the boundary of a polyhedron.
On representation of a solution to a modified Cauchy problem.
On representations of real analytic functions by monogenic functions
Using the method of normalized systems of functions, we study one representation of real analytic functions by monogenic functions (i.e., solutions of Dirac equations), which is an Almansi’s formula of infinite order. As applications of the representation, we construct solutions of the inhomogeneous Dirac and poly-Dirac equations in Clifford analysis.
On second order nonlinear equations with rectilinear characteristics.