The Asymptotics of the Heat Equation for a Boundary Value Problem.
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 Dirichlet boundary conditions and related natural boundary conditions in strengthened Sobolev spaces for discretized parabolic problems.
The existence and uniqueness theorem in Biot's consolidation theory
Existence and uniqueness theorem is established for a variational problem including Biot's model of consolidation of clay. The proof of existence is constructive and uses the compactness method. Error estimates for the approximate solution obtained by a method combining finite elements and Euler's backward method are given.
The fictitious domain method for the mixed finite element approximation of the wave equation
The Fourier spectral method for the Sivashinsky equation.
The version of Eulerian-Lagrangian mixed discontinuous finite element methods for advection-diffusion problems.
The initial value problem for the equations of magnetohydrodynamic type in non-cylindrical domains.
By using the spectral Galerkin method, we prove the existence of weak solutions for a system of equations of magnetohydrodynamic type in non-cylindrical domains.
The Lie-algebraic discrete approximation scheme for evolution equations with Dirichlet/Neumann data.
The lifespan of spherically symmetric solutions of the compressible Euler equations outside an impermeable sphere
The quasi-stationary approximation for the Stefan problem with a convective boundary condition.
The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques
Systems of mixed hyperbolic-elliptic conservation laws can serve as models for the evolution of a liquid-vapor fluid with possible sharp dynamical phase changes. We focus on the equations of ideal hydrodynamics in the isothermal case and introduce a thermodynamically consistent solution of the Riemann problem in one space dimension. This result is the basis for an algorithm of ghost fluid type to solve the sharp-interface model numerically. In particular the approach allows to resolve phase transitions...
Three-level discrete time Galerkin approximations for the non-stationary Navier-Stokes equation
Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equations.
Topological solutions in the self-dual Chern-Simons theory : existence and approximation