On a generalization of the Dirichlet integral.
On a generalization of the Keldysh theorem.
On a generalized heat potential
On a generalized nonlinear equation of Schrödinger type.
On a generalized reflection law for functions satisfying the Helmholtz equation.
On a generalized Stokes problem
We deal with a generalization of the Stokes system. Instead of the Laplace operator, we consider a general elliptic operator and a pressure gradient with small perturbations. We investigate the existence and uniqueness of a solution as well its regularity properties. Two types of regularity are provided. Aside from the classical Hilbert regularity, we also prove the Hölder regularity for coefficients in VMO space.
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 ground state and two symmetric ground state solutions in a domain
On a Hamilton-Jacobi equation
On a heat potential
On a heat potential (Preliminary communication)
On a hierarchical basis multilevel method with nonconforming P1 elements.
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 holomorphic solution of a singular partial differential equation with many simple poles
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 hyperbolic coefficient inverse problem via partial dynamic boundary measurements.
On a inequality of Friedrichs.