Reducing real almost-linear second-order partial differential operators in two independent variables to a canonical form
Reflectionless boundary propagation formulas for partial wave solutions to the wave equation.
Regularity in elliptic free boundary problems. II. Equations of higher order
Remarques sur le problème de Cauchy pour l'équation des ondes
Riesz potentials for Korteweg-de Vries solitons and Sturm-Liouville problems.
Scattering, transformations spectrales et équations d'évolution non linéaires
Similarity and rescaling.
Solutions to time-fractional diffusion-wave equation in cylindrical coordinates.
Suggestion from the Past?
Mathematics Subject Classification: 26A33 (main), 35A22, 78A25, 93A30The generalization of the concept of derivative to non-integer values goes back to the beginning of the theory of differential calculus. Nevertheless, its application in physics and engineering remained unexplored up to the last two decades. Recent research motivated the establishment of strategies taking advantage of the Fractional Calculus (FC) in the modeling and control of many phenomena. In fact, many classical engineering...
Sums of Plane Waves, and the Range of the Random Transform.
Sur les solutions fondamentales d'ordre fini de croissance.
Sur les transformations de Bäcklund
Symmetry of the barochronous motions of a gas.
Systems of multi-dimensional Laplace transforms and a heat equation.
Teoria dei fasci e trasformazioni integrali per -moduli tra varietà di Grassmann
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 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 Fourier method for the linear partial differential equations of the -th order
The Fourier transform on and its application to Cauchy problems for linear partial differential equations
The jump problem for mixed-type equations with defects on the type change line.