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.
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 existence of Ginzburg-Landau solutions on the plane by a direct variational method
The extended tanh-mehtod for finding traveling wave solutions of nonlinear evolution equations.
The FBI transform, operators with nonsmooth coefficients and the nonlinear wave equation
The aim of this work is threefold. First we set up a calculus for partial differential operators with nonsmooth coefficients which is based on the FBI (Fourier-Bros-Iagolnitzer) transform. Then, using this calculus, we prove a weaker version of the Strichartz estimates for second order hyperbolic equations with nonsmooth coefficients. Finally, we apply these new Strichartz estimates to second order nonlinear hyperbolic equations and improve the local theory, i.e. prove local well-posedness for initial...
The fictitious domain method for the mixed finite element approximation of the wave equation
The Fourier method for the linear partial differential equations of the -th order
The Fourier spectral method for the Sivashinsky equation.
The Fourier transform on and its application to Cauchy problems for linear partial differential equations
The Fuchsian Cauchy problem.