On a global classical solution of a quasilinear hyperbolic equation.
On a Global Existence Theorem of Small Amplitude Solutions for Nonlinear Wave Equations in an Exterior Domain.
On a global in time existence theorem of smooth solutions to an nonlinear wave equation with viscosity.
On a high-order iterative scheme for a nonlinear Love equation
In this paper, a high-order iterative scheme is established for a nonlinear Love equation associated with homogeneous Dirichlet boundary conditions. This is a development based on recent results (L. T. P. Ngoc, N. T. Long (2011); L. X. Truong, L. T. P. Ngoc, N. T. Long (2009)) to get a convergent sequence at a rate of order to a local unique weak solution of the above mentioned equation.
On a Local Existence Theorem of Neumann Problem for Some Quasilinear Hyperbolic Systems of 2nd Order.
On a nonlinear coupled system with internal damping.
On a nonlinear equation of the vibrating string
A nonlinear model of the vibrating string is studied and global existence and uniqueness theorems for the solution of the Cauchy-Dirichlet problem are given. The model is then compared to the classical D'Alembert model and to a nonlinear model due to Kirchhoff.
On a nonlinear wave equation in unbounded domains.
On a nonlinear wave equation with damping.
On a parabolic strongly nonlinear problem on manifolds.
On a shock problem involving a nonlinear viscoelastic bar.
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 weakly hyperbolic quasilinear mixed problem of second order
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 exact solutions of a degenerate quasilinear wave equation with source term.
On generalized periodic solutions of some nonlinear telegraph and beam equations
On global behavior of solutions to an inverse problem for semi-linear hyperbolic equations.
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]).