In this paper we study solvability of the Cauchy problem of the Kawahara equation 偏导dtu ＋ au偏导dzu ＋ β偏导d^3xu ＋γ偏导d^5xu = 0 with L^2 initial data. By working on the Bourgain space X^r,s（R^2） associated w...In this paper we study solvability of the Cauchy problem of the Kawahara equation 偏导dtu ＋ au偏导dzu ＋ β偏导d^3xu ＋γ偏导d^5xu = 0 with L^2 initial data. By working on the Bourgain space X^r,s（R^2） associated with this equation, we prove that the Cauchy problem of the Kawahara equation is locally solvable if initial data belong to H^r（R） and -1 〈 r ≤ 0. This result combined with the energy conservation law of the Kawahara equation yields that global solutions exist if initial data belong to L^2（R）.展开更多
This paper studies the multi-dimensional Black-Scholes model of security valnation. The extension of the Black-Scholes model implies; the partial differential equation derived from an absence of arbitrage which the au...This paper studies the multi-dimensional Black-Scholes model of security valnation. The extension of the Black-Scholes model implies; the partial differential equation derived from an absence of arbitrage which the authors solve by using the Feynmeu-Kac Formula. Then they compute its special example by solving the multi-variable partial differential equation.展开更多
The Cauchy problem and initial traces for the doubly degenerate parabolic equationsare studied. Under certain growth condition on the initial datum u0(x) as the existence of solution is proved. The results obtained ar...The Cauchy problem and initial traces for the doubly degenerate parabolic equationsare studied. Under certain growth condition on the initial datum u0(x) as the existence of solution is proved. The results obtained are optimal in the dass of nonnegative locally bounded solution, for which a Harnack-type inequality holds.展开更多
In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial ve...In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.展开更多
The final value problem for the classical coupled Klein-Gordon-Schrodinger equations is studied in . This leads to the construction of the modified wave operator Ω, for certain scattered data. When initial functions ...The final value problem for the classical coupled Klein-Gordon-Schrodinger equations is studied in . This leads to the construction of the modified wave operator Ω, for certain scattered data. When initial functions belong to (Ω) which denotes the range domain of Ω, the global existence and asymptotic behavior of solutions of Cauchy problem tor the coupled Klein-Gordon-Schrodinger equations are proved.展开更多
In this paper, we have established the existence theorem of the weak solution of theboundary problems for systems of ferro-magnetic chain ty means of the viscosity eliminatingmethod and the Leray-Schauder fixed point ...In this paper, we have established the existence theorem of the weak solution of theboundary problems for systems of ferro-magnetic chain ty means of the viscosity eliminatingmethod and the Leray-Schauder fixed point argument.展开更多
基金Project supported by the China National Natural Science Foundation (Grants 10171111, 10171112)
文摘In this paper we study solvability of the Cauchy problem of the Kawahara equation 偏导dtu ＋ au偏导dzu ＋ β偏导d^3xu ＋γ偏导d^5xu = 0 with L^2 initial data. By working on the Bourgain space X^r,s（R^2） associated with this equation, we prove that the Cauchy problem of the Kawahara equation is locally solvable if initial data belong to H^r（R） and -1 〈 r ≤ 0. This result combined with the energy conservation law of the Kawahara equation yields that global solutions exist if initial data belong to L^2（R）.
文摘This paper studies the multi-dimensional Black-Scholes model of security valnation. The extension of the Black-Scholes model implies; the partial differential equation derived from an absence of arbitrage which the authors solve by using the Feynmeu-Kac Formula. Then they compute its special example by solving the multi-variable partial differential equation.
文摘The Cauchy problem and initial traces for the doubly degenerate parabolic equationsare studied. Under certain growth condition on the initial datum u0(x) as the existence of solution is proved. The results obtained are optimal in the dass of nonnegative locally bounded solution, for which a Harnack-type inequality holds.
基金supported by National Natural Science Foundation of China (Grant No.10671124)
文摘In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.
基金the National Natural Science Foundation of China
文摘The final value problem for the classical coupled Klein-Gordon-Schrodinger equations is studied in . This leads to the construction of the modified wave operator Ω, for certain scattered data. When initial functions belong to (Ω) which denotes the range domain of Ω, the global existence and asymptotic behavior of solutions of Cauchy problem tor the coupled Klein-Gordon-Schrodinger equations are proved.
基金Project supported by the National Natural, Science Foundation of China and CAEP.
文摘In this paper, we have established the existence theorem of the weak solution of theboundary problems for systems of ferro-magnetic chain ty means of the viscosity eliminatingmethod and the Leray-Schauder fixed point argument.
