Some new estimations of scalar products of vector fields in unbounded domains are investigated. Lp-estimations for the vector fields were proved in special weighted functional spaces. The paper generalizes our earlier...Some new estimations of scalar products of vector fields in unbounded domains are investigated. Lp-estimations for the vector fields were proved in special weighted functional spaces. The paper generalizes our earlier results for bounded domains. Estimations for scalar products make it possible to investigate wide classes of mathematical physics problems in physically inhomogeneous domains. Such estimations allow studying issues of correctness for problems with non-smooth coefficients. The paper analyses solvability of stationary set of Maxwell equations in inhomogeneous unbounded domains based on the proved Lp-estimations.展开更多
Using the Hartle-Hawking method, we discuss the quantum Cosmology with O_(8N+1)^-symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calc...Using the Hartle-Hawking method, we discuss the quantum Cosmology with O_(8N+1)^-symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calculated. We got the material solution of the cosmic wave function in harmonic eigenstate, and the solution of space is the product of the Gauss factor and one polynomial. After analysing the wave function of the universe under the quantum effect, we found that the probability density of the universe appearing at a=0 is zero, and that the minimal radius of the ground state of the universe is on the Planck scale. The analysis of the wave function of the universe, also reveals that at the very early stage of the universe the probability density of the multl-scalar field is smaller than that of the onescalar field.展开更多
Using a Gurevich-Krylov solution that describes the propagation of nonlinear magnetoacoustic waves in a cold plasma, we construct solutions of various other nonlinear systems. These include, for example, Madelung flui...Using a Gurevich-Krylov solution that describes the propagation of nonlinear magnetoacoustic waves in a cold plasma, we construct solutions of various other nonlinear systems. These include, for example, Madelung fluid, reaction diffusion, Broer-Kaup, Boussinesq, and Hamilton-Jacobi-Bellman systems. We also construct dilaton field solutions for a Jackiw-Teitelboim black hole with a negative cosmological constant. The black hole metric corresponds to a cold plasma metric by way of a change of variables, and the plasma dilatons and cosmological constant also have an expression in terms of parameters occurring in the Gurevich-Krylov solution. A dispersion relation, moreover, links the magnetoacoustic system and a resonance nonlinear Schr<span style="white-space:nowrap;">ö</span>dinger equation.展开更多
Massive scalar fields are considered in with a global monopole in f（R） gravity. The exact background is obtained and is given in terms of the Heun functions to study the Hawking radiation and the gravitational field...Massive scalar fields are considered in with a global monopole in f（R） gravity. The exact background is obtained and is given in terms of the Heun functions to study the Hawking radiation and the gravitational field produced by a Schwarzschild black hole solution of the radial part of the Klein-Gordon equation in this general Heun functions. We apply the properties of the general the resonant frequencies of scalar particles.展开更多
文摘Some new estimations of scalar products of vector fields in unbounded domains are investigated. Lp-estimations for the vector fields were proved in special weighted functional spaces. The paper generalizes our earlier results for bounded domains. Estimations for scalar products make it possible to investigate wide classes of mathematical physics problems in physically inhomogeneous domains. Such estimations allow studying issues of correctness for problems with non-smooth coefficients. The paper analyses solvability of stationary set of Maxwell equations in inhomogeneous unbounded domains based on the proved Lp-estimations.
基金Project supported by the National Natural Science Foundation of China.
文摘Using the Hartle-Hawking method, we discuss the quantum Cosmology with O_(8N+1)^-symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calculated. We got the material solution of the cosmic wave function in harmonic eigenstate, and the solution of space is the product of the Gauss factor and one polynomial. After analysing the wave function of the universe under the quantum effect, we found that the probability density of the universe appearing at a=0 is zero, and that the minimal radius of the ground state of the universe is on the Planck scale. The analysis of the wave function of the universe, also reveals that at the very early stage of the universe the probability density of the multl-scalar field is smaller than that of the onescalar field.
文摘Using a Gurevich-Krylov solution that describes the propagation of nonlinear magnetoacoustic waves in a cold plasma, we construct solutions of various other nonlinear systems. These include, for example, Madelung fluid, reaction diffusion, Broer-Kaup, Boussinesq, and Hamilton-Jacobi-Bellman systems. We also construct dilaton field solutions for a Jackiw-Teitelboim black hole with a negative cosmological constant. The black hole metric corresponds to a cold plasma metric by way of a change of variables, and the plasma dilatons and cosmological constant also have an expression in terms of parameters occurring in the Gurevich-Krylov solution. A dispersion relation, moreover, links the magnetoacoustic system and a resonance nonlinear Schr<span style="white-space:nowrap;">ö</span>dinger equation.
基金funded by the Brazilian research agencies CNPq(research Project No.140612/2014-9)CAPES(PDSE Process No.88881.133092/2016-01)+1 种基金funded by the CNPq through the research Project No.150565/2016-0partially supported by the CNPq through the research Project No.304553/2010-7
文摘Massive scalar fields are considered in with a global monopole in f（R） gravity. The exact background is obtained and is given in terms of the Heun functions to study the Hawking radiation and the gravitational field produced by a Schwarzschild black hole solution of the radial part of the Klein-Gordon equation in this general Heun functions. We apply the properties of the general the resonant frequencies of scalar particles.
