In the paper, by using the methods of compensated compactness and energy estimate, the convergence of class of fourth and sixth orders singular perturbed, partial differential equations is obtained, and furthermore, t...In the paper, by using the methods of compensated compactness and energy estimate, the convergence of class of fourth and sixth orders singular perturbed, partial differential equations is obtained, and furthermore, the regularity of solutions are improved.展开更多
In this paper we prove that the Jacobian J（F） of a map F（f1,…,f1 from Ginto Rt maps the product of Lebesgue space Lp1×…× Lp1 into local Hardy space hY（G）,whereQ/Q＋1〈r〈1,and Q is the homogeneous dim...In this paper we prove that the Jacobian J（F） of a map F（f1,…,f1 from Ginto Rt maps the product of Lebesgue space Lp1×…× Lp1 into local Hardy space hY（G）,whereQ/Q＋1〈r〈1,and Q is the homogeneous dimension of the stratified Lie group G.展开更多
In this paper, we study the following Cauchy problem.and obtain the convergence of L bounded approximating Sequences generated by the methodof vanishing viscidity and compensated compactness.
In this article, we develop a new technique to prove the global existene of entropy solutions to an inhomogeneous isentropic compressible Euler equations through the compensated compactness and vanishing viscosity met...In this article, we develop a new technique to prove the global existene of entropy solutions to an inhomogeneous isentropic compressible Euler equations through the compensated compactness and vanishing viscosity method. In particular, the entropy solutions are uniformly bounded independent of time.展开更多
In this paper, a compensated compactness framework is established for sonicsubsonic approximate solutions to the n-dimensional （n ≥ 2） Euler equations for steady irrotational flow that may contain stagnation points...In this paper, a compensated compactness framework is established for sonicsubsonic approximate solutions to the n-dimensional （n ≥ 2） Euler equations for steady irrotational flow that may contain stagnation points. This compactness framework holds provided that the approximate solutions are uniformly bounded and satisfy Hloc^-1（Ω） compactness conditions. As illustration, we show the existence of sonic-subsonic weak solution to n-dimensional （n ≥ 2） Euler equations for steady irrotational flow past obstacles or through an infinitely long nozzle. This is the first result concerning the sonic-subsonic limit for n-dimension （n ≥ 3）.展开更多
In this article, we give the existence of global L∞bounded entropy solutions to the Cauchy problem of a generalized n × n hyperbolic system of Le Roux type. The main difficulty lies in establishing some compactn...In this article, we give the existence of global L∞bounded entropy solutions to the Cauchy problem of a generalized n × n hyperbolic system of Le Roux type. The main difficulty lies in establishing some compactness estimates of the viscosity solutions because the system has been generalized from 2×2 to n×n and more linearly degenerate characteristic fields emerged, and the emergence of singularity in the region {v1= 0} is another difficulty.We obtain the existence of the global weak solutions using the compensated compactness method coupled with the construction of entropy-entropy flux and BV estimates on viscous solutions.展开更多
Based on the framework introduced in [4] or [5], the singular limits of stiff relaxation and dominant diffusion for the Cauchy problem of inhomogeneous equations of elasticity is studied. We are able to reach equilibr...Based on the framework introduced in [4] or [5], the singular limits of stiff relaxation and dominant diffusion for the Cauchy problem of inhomogeneous equations of elasticity is studied. We are able to reach equilibrium even though the nonlinear stress term is not strictly increasing.展开更多
By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturb...By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.展开更多
In this paper we study the homogenization of degenerate quasilinear parabolicequations: (partial deriv)_tu - diva (t/ε, x/ε, u, ▽u) = f(t,x), where a(t, y, α, λ) isperiodic in (t,y).
In this paper, we propose a model in studying soft ferromagnetic films, which is readily accessible experimentally. By using penalty approximation and compensated compactness, we prove that the dynamical equation in t...In this paper, we propose a model in studying soft ferromagnetic films, which is readily accessible experimentally. By using penalty approximation and compensated compactness, we prove that the dynamical equation in thin film has a local weak solution. Moreover, the corresponding linear equation is also dealt with in great detail.展开更多
文摘In the paper, by using the methods of compensated compactness and energy estimate, the convergence of class of fourth and sixth orders singular perturbed, partial differential equations is obtained, and furthermore, the regularity of solutions are improved.
文摘In this paper we prove that the Jacobian J（F） of a map F（f1,…,f1 from Ginto Rt maps the product of Lebesgue space Lp1×…× Lp1 into local Hardy space hY（G）,whereQ/Q＋1〈r〈1,and Q is the homogeneous dimension of the stratified Lie group G.
文摘In this paper, we study the following Cauchy problem.and obtain the convergence of L bounded approximating Sequences generated by the methodof vanishing viscidity and compensated compactness.
基金supported in part by NSFC Grant No.11371349supported in part by NSFC Grant No.11541005Shandong Provincial Natural Science Foundation(ZR2015AM001)
文摘In this article, we develop a new technique to prove the global existene of entropy solutions to an inhomogeneous isentropic compressible Euler equations through the compensated compactness and vanishing viscosity method. In particular, the entropy solutions are uniformly bounded independent of time.
基金supported in part by NSFC (10825102) for distinguished youth scholarNational Basic Research Program of China (973 Program) under Grant No.2011CB808002
文摘In this paper, a compensated compactness framework is established for sonicsubsonic approximate solutions to the n-dimensional （n ≥ 2） Euler equations for steady irrotational flow that may contain stagnation points. This compactness framework holds provided that the approximate solutions are uniformly bounded and satisfy Hloc^-1（Ω） compactness conditions. As illustration, we show the existence of sonic-subsonic weak solution to n-dimensional （n ≥ 2） Euler equations for steady irrotational flow past obstacles or through an infinitely long nozzle. This is the first result concerning the sonic-subsonic limit for n-dimension （n ≥ 3）.
基金supported by the National Science Foundation of China(11572148,11671193)the National Research Foundation for the Doctoral Program of Higher Education of China(20133218110025)
文摘In this article, we give the existence of global L∞bounded entropy solutions to the Cauchy problem of a generalized n × n hyperbolic system of Le Roux type. The main difficulty lies in establishing some compactness estimates of the viscosity solutions because the system has been generalized from 2×2 to n×n and more linearly degenerate characteristic fields emerged, and the emergence of singularity in the region {v1= 0} is another difficulty.We obtain the existence of the global weak solutions using the compensated compactness method coupled with the construction of entropy-entropy flux and BV estimates on viscous solutions.
文摘Based on the framework introduced in [4] or [5], the singular limits of stiff relaxation and dominant diffusion for the Cauchy problem of inhomogeneous equations of elasticity is studied. We are able to reach equilibrium even though the nonlinear stress term is not strictly increasing.
基金Supported by the Innovation Talents of Science and Technology of Henan University(2009-HASTIT-007)Supported by the Natural Science Program of Department of Education(2011A110006)
文摘By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.
基金Supported by the Key Teachers Foundation of Chongqing University (No.2003018)the Key Teachers Foundation of Universities in Chongqing (No.20020126)
文摘In this paper we study the homogenization of degenerate quasilinear parabolicequations: (partial deriv)_tu - diva (t/ε, x/ε, u, ▽u) = f(t,x), where a(t, y, α, λ) isperiodic in (t,y).
基金the National Natural Science Foundation of China(No.10171113,10471156)(Tianyuan Foundation 10526040)Guangdong Provincial Natural Science Foundation(No.4009793)
文摘In this paper, we propose a model in studying soft ferromagnetic films, which is readily accessible experimentally. By using penalty approximation and compensated compactness, we prove that the dynamical equation in thin film has a local weak solution. Moreover, the corresponding linear equation is also dealt with in great detail.
