On exact solutions of a degenerate quasilinear wave equation with source term.
On existence and uniqueness of solutions of nonlocal problems for hyperbolic differential-functional equations in two independent variables
We seek for classical solutions to hyperbolic nonlinear partial differential-functional equations of the second order. We give two theorems on existence and uniqueness for problems with nonlocal conditions in bounded and unbounded domains.
On generalized periodic solutions of some nonlinear telegraph and beam equations
On generalized solutions to the wave equation in canonical form [Book]
On geometry of fronts in wave propagations
We give a geometric descriptions of (wave) fronts in wave propagation processes. Concrete form of defining function of wave front issued from initial algebraic variety is obtained by the aid of Gauss-Manin systems associated with certain complete intersection singularities. In the case of propagations on the plane, we get restrictions on types of possible cusps that can appear on the wave front.
On global behavior of solutions to an inverse problem for semi-linear hyperbolic equations.
On global real analytic solutions of the degenerate Kirchhoff equation
On global solutions to a defocusing semi-linear wave equation.
We prove that the 3D cubic defocusing semi-linear wave equation is globally well-posed for data in the Sobolev space Hs where s > 3/4. This result was obtained in [11] following Bourgain's method ([3]). We present here a different and somewhat simpler argument, inspired by previous work on the Navier-Stokes equations ([4, 7]).
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 initial boundary value problem with Dirichlet integral conditions for a hyperbolic equation with the Bessel operator.
On Kakeya–Nikodym averages, -norms and lower bounds for nodal sets of eigenfunctions in higher dimensions
We extend a result of the second author [27, Theorem 1.1] to dimensions which relates the size of -norms of eigenfunctions for to the amount of -mass in shrinking tubes about unit-length geodesics. The proof uses bilinear oscillatory integral estimates of Lee [22] and a variable coefficient variant of an " removal lemma" of Tao and Vargas [35]. We also use Hörmander’s [20] oscillatory integral theorem and the Cartan–Hadamard theorem to show that, under the assumption of nonpositive curvature,...
On -estimates for hyperbolic systems
On -estimates for the Cauchy problem for hyperbolic systems (Preliminary communication)
On Lars Hörmander’s remark on the characteristic Cauchy problem
We extend the results of a work by L. Hörmander [9] concerning the resolution of the characteristic Cauchy problem for second order wave equations with regular first order potentials. The geometrical background of this work was a spatially compact spacetime with smooth metric. The initial data surface was spacelike or null at each point and merely Lipschitz. We lower the regularity hypotheses on the metric and potential and obtain similar results. The Cauchy problem for a spacelike initial data...
On L...-decay and scattering for nonlinear Klein-Gordon equations.
On Lipschitz continuity of the solution map for two-dimensional wave maps
On Lp - Lp' Estimates for the Wave Equation.
On M. Kac's probabilistic formula for the solution of the telegraphist's equation
On Maxwell equations with the Preisach hysteresis operator: The one- dimensional time-periodic case
Energy functionals for the Preisach hysteresis operator are used for proving the existence of weak periodic solutions of the one-dimensional systems of Maxwell equations with hysteresis for not too large right-hand sides. The upper bound for the speed of propagation of waves is independent of the hysteresis operator.
On measure solutions to the zero-pressure gas model and their uniqueness