On a strong solution in the method of spherical harmonics for a nonstationary transport equation.
On a supplementary conservation law for a hyperbolic model of heat conductor
In the context of the wave propagation theory in nonlinear hyperbolic systems, we analyse, in the case of a rigid heat conductor, the model proposed by G. Grioli. After introducing the constitutive relations according to the point of view of the extended thermodynamics, we look for the compatibility of the governing equations with a supplementary conservation law. We obtain the functional form of the constitutive quantities and we are able to show that the governing equations may be written in symmetric...
On a system of nonlinear wave equations with the Kirchhoff-Carrier and Balakrishnan-Taylor terms
We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions.
On a variational inequality for the nonhomogeneous degenerated Kirchhoff equation with a frictional damping.
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.