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 hybrid finite-volume-particle method
We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the one- and two-dimensional Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. This paper is an extension of our previous work [Chertock, Kurganov and Petrova, J. Sci. Comput. (to appear)], where the one-dimensional finite-volume-particle method has been proposed. The core idea behind the...
On a hybrid finite-volume-particle method
We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the one- and two-dimensional Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. This paper is an extension of our previous work [Chertock, Kurganov and Petrova, J. Sci. Comput. (to appear)], where the one-dimensional finite-volume-particle method has been proposed. The core idea behind the...
On a Kirchhoff-Carrier equation with nonlinear terms containing a finite number of unknown values
We consider problem (P) of Kirchhoff-Carrier type with nonlinear terms containing a finite number of unknown values with By applying the linearization method together with the Faedo-Galerkin method and the weak compact method, we first prove the existence and uniqueness of a local weak solution of problem (P). Next, we consider a specific case of (P) in which the nonlinear term contains the sum . Under suitable conditions, we prove that the solution of converges to the solution of the corresponding...
On a linear hyperbolic equation with smooth coefficients without solutions
An example of a locally unsolvable hyperbolic equation of the second order is constructed, which has smooth () coefficients, but has no solutions in the class of distributions.
On a Local Existence Theorem of Neumann Problem for Some Quasilinear Hyperbolic Systems of 2nd Order.
On a mixed boundary values problem for Lavrentev type equations
On a mixed nonlocal problem for a wave equation.
On a new superposition principle for optimization problem
On a nonlinear coupled system with internal damping.
On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient.
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 phase-field model with a logarithmic nonlinearity
Our aim in this paper is to study the existence of solutions to a phase-field system based on the Maxwell-Cattaneo heat conduction law, with a logarithmic nonlinearity. In particular, we prove, in one and two space dimensions, the existence of a solution which is separated from the singularities of the nonlinear term.
On a scalar conservation law with nonlinear diffusion and linear dispersion in heterogeneous media.
On a shock problem involving a nonlinear viscoelastic bar.
On a spatial problem of Darboux type for a second-order hyperbolic equation.