On a Volterra Stieltjes integral equation.
On a weakly hyperbolic equation with a term of order zero
On a weakly hyperbolic quasilinear mixed problem of second order
On an inequality in nonlinear thermoelasticity.
On an inverse problem for a linear hyperbolic integrodifferential equation.
On an ODE Relevant for the General Theory of the Hyperbolic Cauchy Problem
2000 Mathematics Subject Classification: 34E20, 35L80, 35L15.In this paper we study an ODE in the complex plane. This is a key step in the search of new necessary conditions for the well posedness of the Cauchy Problem for hyperbolic operators with double characteristics.
On anisotropic, dispersive and dissipative wave equations
On asymptotic behavior of global solutions for hyperbolic hemivariational inequalities.
On bilinear estimates for wave equations
I will start with a short review of the classical restriction theorem for the sphere and Strichartz estimates for the wave equation. I then plan to give a detailed presentation of their recent generalizations in the form of “Bilinear Estimates”. In addition to the theory, which is now quite well developed, I plan to discuss a more general point of view concerning the theory. By investigating simple examples I will derive necessary conditions for such estimates to be true. I also plan to discuss...
On bilinear restriction type estimates and applications to nonlinear wave equations
I will start with a short review of the classical restriction theorem for the sphere and Strichartz estimates for the wave equation. I then plan to give a detailed presentation of their recent generalizations in the form of “bilinear estimates”. In addition to the theory, which is now quite well developed, I plan to discuss a more general point of view concerning the theory. By investigating simple examples I will derive necessary conditions for such estimates to be true. I also plan to discuss...
On closed-form solutions of some nonlinear partial differential equations.
On Composite Mesh Difference Methods for Hyperbolic Differential Equations.
On construction of weak solutions with higher integrable gradients to linear hyperbolic partial differential systems
On continuous solutions to linear hyperbolic systems
We study the conditions under which the Cauchy problem for a linear hyperbolic system of partial differential equations of the first order in two independent variables has a unique continuous solution (not necessarily Lipschitz continuous). In addition to obvious continuity assumptions on coefficients and initial data, the sufficient conditions are the bounded variation of the left eigenvectors along the characteristic curves.
On counting the number of eigenvalues in the right half-plane for spectral problems connected with hyperbolic systems. II: Differential equations.
On error estimates in the Galerkin method for hyperbolic equations.
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