In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional（m-D） conservation law with unbounded initial value; our metho...In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional（m-D） conservation law with unbounded initial value; our methods are new and essentially different with the situation of bounded initial value.展开更多
This paper is concerned with the simple waves of a kind of two dimensional hyperbolic system of conservation laws,which can be obtained from the two dimensional relativistic membrane equation in Minkowski space.Using ...This paper is concerned with the simple waves of a kind of two dimensional hyperbolic system of conservation laws,which can be obtained from the two dimensional relativistic membrane equation in Minkowski space.Using wave decomposition method,we get that a flow adjacent to a nonconstant state can be a global simple wave.Furthermore,the flow is covered by three families of characteristics,in which the first family of characteristics is straight and the others are curved,which is different to the almost related results.展开更多
In this paper, we investigate a class of mixed initial-boundary value problems for a kind of n × n quasilinear hyperbolic systems of conservation laws on the quarter plan. We show that the structure of the pieeew...In this paper, we investigate a class of mixed initial-boundary value problems for a kind of n × n quasilinear hyperbolic systems of conservation laws on the quarter plan. We show that the structure of the pieeewise C^1 solution u = u（t, x） of the problem, which can be regarded as a perturbation of the corresponding Riemann problem, is globally similar to that of the solution u = U（x/t） of the corresponding Riemann problem. The piecewise C^1 solution u = u（t, x） to this kind of problems is globally structure-stable if and only if it contains only non-degenerate shocks and contact discontinuities, but no rarefaction waves and other weak discontinuities.展开更多
This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a con...This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a constant function. Under the condition that the flux function has a finite number of weak discontinuous points, by using the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method to the global weak entropy solution for this initial-boundary value problem, and by investigating the interaction of elementary waves and the boundary, we clarify the geometric structure and the behavior of boundary for the weak entropy solution.展开更多
This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space R+= {x |x > 0} where a>0 , u(x,t) is an unknown function of x ∈ R+ and t>0 , u ± , um ar...This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space R+= {x |x > 0} where a>0 , u(x,t) is an unknown function of x ∈ R+ and t>0 , u ± , um are three given constants satisfying um=u+≠u- or um=u-≠u+ , and the flux function f is a given continuous function with a weak discontinuous point ud. The main purpose of our present manuscript is devoted to studying the structure of the global weak entropy solution for the above initial-boundary value problem under the condition of f '-(ud) > f '+(ud). By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial-boundary value problem, and investigate the interaction of elementary waves with the boundary and the boundary behavior of the weak entropy solution.展开更多
Civilization has reached such a level of development when the energy produced by humanity (the energy of civilization) begins to become a noticeable addition to the energy of incoming solar radiation. The energy of ci...Civilization has reached such a level of development when the energy produced by humanity (the energy of civilization) begins to become a noticeable addition to the energy of incoming solar radiation. The energy of civilization accumulates in the surface layer, where human activity is concentrated, and dissipates in the form of heat, causing a rise in temperature. An equation is derived to calculate the contribution of civilization’s energy to global warming, which prove to be directly proportional to the accumulated energy of civilization and inversely proportional to the energy of solar radiation on the earth’s surface to the power of three-fourths. The coefficient of proportionality is expressed in terms of fundamental physical constants: Planck’s constant, the speed of light and the Boltzmann constant. It is shown that the contribution of energy of civilization is comparable with the role of increasing concentration of carbon dioxide over the past decades. To mitigate the negative effect, it is necessary to reduce the energy production and partially revise the environmental policy.展开更多
We present (on the 13<sup>th</sup> International Conference on Geology and Geophysics) the convincing evidence that the strongest earthquakes (according to the U.S. Geological Survey) of the Earth (during ...We present (on the 13<sup>th</sup> International Conference on Geology and Geophysics) the convincing evidence that the strongest earthquakes (according to the U.S. Geological Survey) of the Earth (during the range 2020 - 2023 AD) occurred near the predicted (calculated in advance based on the global prediction thermohydrogravidynamic principles determining the maximal temporal intensifications of the global seismotectonic, volcanic, climatic and magnetic processes of the Earth) dates 2020.016666667 AD (Simonenko, 2020), 2021.1 AD (Simonenko, 2019, 2020), 2022.18333333 AD (Simonenko, 2021), 2023.26666666 AD (Simonenko, 2022) and 2020.55 AD, 2021.65 AD (Simonenko, 2019, 2021), 2022.716666666 AD (Simonenko, 2022), respectively, corresponding to the local maximal and to the local minimal, respectively, combined planetary and solar integral energy gravitational influences on the internal rigid core of the Earth. We present the short-term thermohydrogravidynamic technology (based on the generalized differential formulation of the first law of thermodynamics and the first global prediction thermohydrogravidynamic principle) for evaluation of the maximal magnitude of the strongest (during the March, 2023 AD) earthquake of the Earth occurred on March 16, 2023 AD (according to the U.S. Geological Survey). .展开更多
The world is facing the third important global power shift.The United States,EU, Japan,Russia,China,and the newly emerging power group are becoming the six big forces in the international center stage,while the former...The world is facing the third important global power shift.The United States,EU, Japan,Russia,China,and the newly emerging power group are becoming the six big forces in the international center stage,while the former three forces and the latter three belong to two groups,waning and waxing respectively.The major shift in the global balance of power is bound to give rise to the transitional multi-polar configuration,which implies a shifting of leadership over the configuration,China and U.S.outweighing other forces,global issues looming large,homogeneity blending with heterogeneity,and a shifting center of world powers.The transitional multi-polar configuration is all about change,upon which China is one of the decisive forces.展开更多
基金partly supported by Natural Science Foundation of China(11471332 and 11071246)
文摘In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional（m-D） conservation law with unbounded initial value; our methods are new and essentially different with the situation of bounded initial value.
文摘This paper is concerned with the simple waves of a kind of two dimensional hyperbolic system of conservation laws,which can be obtained from the two dimensional relativistic membrane equation in Minkowski space.Using wave decomposition method,we get that a flow adjacent to a nonconstant state can be a global simple wave.Furthermore,the flow is covered by three families of characteristics,in which the first family of characteristics is straight and the others are curved,which is different to the almost related results.
基金supported by the National Natural Science Foundation of China under Grant No.10671124
文摘In this paper, we investigate a class of mixed initial-boundary value problems for a kind of n × n quasilinear hyperbolic systems of conservation laws on the quarter plan. We show that the structure of the pieeewise C^1 solution u = u（t, x） of the problem, which can be regarded as a perturbation of the corresponding Riemann problem, is globally similar to that of the solution u = U（x/t） of the corresponding Riemann problem. The piecewise C^1 solution u = u（t, x） to this kind of problems is globally structure-stable if and only if it contains only non-degenerate shocks and contact discontinuities, but no rarefaction waves and other weak discontinuities.
文摘This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a constant function. Under the condition that the flux function has a finite number of weak discontinuous points, by using the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method to the global weak entropy solution for this initial-boundary value problem, and by investigating the interaction of elementary waves and the boundary, we clarify the geometric structure and the behavior of boundary for the weak entropy solution.
文摘This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space R+= {x |x > 0} where a>0 , u(x,t) is an unknown function of x ∈ R+ and t>0 , u ± , um are three given constants satisfying um=u+≠u- or um=u-≠u+ , and the flux function f is a given continuous function with a weak discontinuous point ud. The main purpose of our present manuscript is devoted to studying the structure of the global weak entropy solution for the above initial-boundary value problem under the condition of f '-(ud) > f '+(ud). By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial-boundary value problem, and investigate the interaction of elementary waves with the boundary and the boundary behavior of the weak entropy solution.
文摘Civilization has reached such a level of development when the energy produced by humanity (the energy of civilization) begins to become a noticeable addition to the energy of incoming solar radiation. The energy of civilization accumulates in the surface layer, where human activity is concentrated, and dissipates in the form of heat, causing a rise in temperature. An equation is derived to calculate the contribution of civilization’s energy to global warming, which prove to be directly proportional to the accumulated energy of civilization and inversely proportional to the energy of solar radiation on the earth’s surface to the power of three-fourths. The coefficient of proportionality is expressed in terms of fundamental physical constants: Planck’s constant, the speed of light and the Boltzmann constant. It is shown that the contribution of energy of civilization is comparable with the role of increasing concentration of carbon dioxide over the past decades. To mitigate the negative effect, it is necessary to reduce the energy production and partially revise the environmental policy.
文摘We present (on the 13<sup>th</sup> International Conference on Geology and Geophysics) the convincing evidence that the strongest earthquakes (according to the U.S. Geological Survey) of the Earth (during the range 2020 - 2023 AD) occurred near the predicted (calculated in advance based on the global prediction thermohydrogravidynamic principles determining the maximal temporal intensifications of the global seismotectonic, volcanic, climatic and magnetic processes of the Earth) dates 2020.016666667 AD (Simonenko, 2020), 2021.1 AD (Simonenko, 2019, 2020), 2022.18333333 AD (Simonenko, 2021), 2023.26666666 AD (Simonenko, 2022) and 2020.55 AD, 2021.65 AD (Simonenko, 2019, 2021), 2022.716666666 AD (Simonenko, 2022), respectively, corresponding to the local maximal and to the local minimal, respectively, combined planetary and solar integral energy gravitational influences on the internal rigid core of the Earth. We present the short-term thermohydrogravidynamic technology (based on the generalized differential formulation of the first law of thermodynamics and the first global prediction thermohydrogravidynamic principle) for evaluation of the maximal magnitude of the strongest (during the March, 2023 AD) earthquake of the Earth occurred on March 16, 2023 AD (according to the U.S. Geological Survey). .
文摘The world is facing the third important global power shift.The United States,EU, Japan,Russia,China,and the newly emerging power group are becoming the six big forces in the international center stage,while the former three forces and the latter three belong to two groups,waning and waxing respectively.The major shift in the global balance of power is bound to give rise to the transitional multi-polar configuration,which implies a shifting of leadership over the configuration,China and U.S.outweighing other forces,global issues looming large,homogeneity blending with heterogeneity,and a shifting center of world powers.The transitional multi-polar configuration is all about change,upon which China is one of the decisive forces.
