The Riemann method for equations with leading partial derivative in .
The Riemann problem for a class of resonant hyperbolic systems of balance laws
The Riemann problem for -systems with continuous flux function
The Riemann problem in gasdynamics.
The Riemann-Roch theorem for elliptic operators and solvability of elliptic equations with additional conditions on compact subsets
The Robbins problem for elliptic equations in space
The role of center manifolds in ordinary differential equations
The Role of Green’s Functions in Inverse Scattering at Fixed Energy
The role of oscillations in the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations
Corresponding to the wellposedness result [2] for the classical 3-D Navier-Stokes equations with initial data in the scaling invariant Besov space, here we consider a similar problem for the 3-D anisotropic Navier-Stokes equations where the vertical viscosity is zero. In order to do so, we first introduce the Besov-Sobolev type spaces, and Then with initial data in the scaling invariant space we prove the global wellposedness for provided the norm of initial data is small enough compared...
The role of symmetry and separation in surface evolution and curve shortening.
The role of the boundary in some semilinear Neumann problems
The role of the Lagrange constant in some nonlinear waves equations.
The Rothe method and time periodic solutions to the Navier-Stokes equations and equations of magnetohydrodynamics
The existence of a periodic solution of a nonlinear equation is proved. The theory developed may be used to prove the existence of a periodic solution of the variational formulation of the Navier-Stokes equations or the equations of magnetohydrodynamics. The proof of the main existence theorem is based on Rothe method in combination with the Galerkin method, using the Brouwer fixed point theorem.
The ROTHE method for nonlinear hyperbolic problems
The Rothe method for solving the first initial-boundary value problem for the equation of filtration in a cracked porous medium.
The Rothe method for the McKendrick-von Foerster equation
We present the Rothe method for the McKendrick-von Foerster equation with initial and boundary conditions. This method is well known as an abstract Euler scheme in extensive literature, e.g. K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, Reidel, Dordrecht, 1982. Various Banach spaces are exploited, the most popular being the space of bounded and continuous functions. We prove the boundedness of approximate solutions and stability of the Rothe method in and...
The Rothe's method to a parabolic integrodifferential equation with a nonclassical boundary conditions.
The Runge-Kutta local projection -discontinuous-Galerkin finite element method for scalar conservation laws
The scalar Oseen operator in
This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in theory.
The Scattering of Classical Waves from Inhomogeneous media.