On a new class of generalized solutions for the Stokes equations in exterior domains
On a new superposition principle for optimization problem
On a non-homogeneous shallow-water problem
On a nonlocal problem for a confined plasma in a Tokamak
The paper deals with a nonlocal problem related to the equilibrium of a confined plasma in a Tokamak machine. This problem involves terms and , which are neither local, nor continuous, nor monotone. By using the Galerkin approximate method and establishing some properties of the decreasing rearrangement, we prove the existence of solutions to such problem.
On a non-stationary free boundary transmission problem with continuous extraction and convection, arising in industrial processes
The existence of a weak solution of a non-stationary free boundary transmission problem arising in the production of industrial materials is established. The process is governed by a coupled system involving the Navier--Stokes equations and a non-linear heat equation. The stationary case was studied in [7].
On a possibility of generalization of the Hopf lemma to the case of the Navier-Stokes system with nonzero flows.
On a problem of shallow water type.
On a regularizing effect of Schrödinger type groups
On a seawater intrusion problem.
On a semilinear variational problem
We provide a detailed analysis of the minimizers of the functional , , subject to the constraint . This problem,e.g., describes the long-time behavior of the parabolic Anderson in probability theory or ground state solutions of a nonlinear Schrödinger equation. While existence can be proved with standard methods, we show that the usual uniqueness results obtained with PDE-methods can be considerably simplified by additional variational arguments. In addition, we investigate qualitative properties...
On a semilinear variational problem
We provide a detailed analysis of the minimizers of the functional , , subject to the constraint . This problem, e.g., describes the long-time behavior of the parabolic Anderson in probability theory or ground state solutions of a nonlinear Schrödinger equation. While existence can be proved with standard methods, we show that the usual uniqueness results obtained with PDE-methods can be considerably simplified by additional variational arguments. In addition, we investigate qualitative properties...
On a steady flow in a three-dimensional infinite pipe
The paper examines the steady Navier-Stokes equations in a three-dimensional infinite pipe with mixed boundary conditions (Dirichlet and slip boundary conditions). The velocity of the fluid is assumed to be constant at infinity. The main results show the existence of weak solutions with no restriction on smallness of the flux vector and boundary conditions.
On a stochastic Korteweg-de Vries equation with homogeneous noise
On a strong solution in the method of spherical harmonics for a nonstationary transport equation.
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 Trace Functional for Formal Pseudo-Differential Operators and the Symplectic Structure of the Korteweg-Devries Type Equation.
On a two-dimensional magnetohydrodynamic problem. I. Modelling and analysis
On a variational method for solving hydrodynamical free boundary problems.
On a vibration of an elastic cusped bars.
On a Whitham-type equation.