Philos Trans A Math Phys Eng Sci
August 2024
We consider the new boundary value problem for the generalized Boussinesq model of heat transfer under the inhomogeneous Dirichlet boundary condition for the velocity and under mixed boundary conditions for the temperature. It is assumed that the viscosity, thermal conductivity and buoyancy force in the model equations, as well as the heat exchange boundary coefficient, depend on the temperature. The mathematical apparatus for studying the inhomogeneous boundary value problem under study based on the variational method is being developed.
View Article and Find Full Text PDFA method is presented for solving the characteristic initial-value problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method generalizes the monodromy-transform approach to fields with nonanalytic behavior on the characteristics inherent to waves with distinct wave fronts. The crux of the method is in a reformulation of the main nonlinear symmetry reduced field equations as linear integral equations whose solutions are determined by generalized ("dynamical") monodromy data which evolve from data specified on the initial characteristics (the wave fronts).
View Article and Find Full Text PDFFor space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational functions of an auxiliary complex parameter. They are constructed using the so-called "monodromy transform" approach and our new method for the solution of the linear singular integral equation form of the reduced Einstein equations.
View Article and Find Full Text PDF