Yongqin Liu
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Yongqin Liu has a total of 3 co-authors. Here are the top co-authors by number of shared publications:
- Shuichi Kawashima
Faculty of Mathematics, Kyushu University, Fukuoka, Japan
5 shared publications - Weike Wang
School of Mathematical Sciences, CMA-Shanghai, Shanghai Jiao Tong University, Shanghai, PR China
2 shared publications - Yi Zhou
Fudan University
1 shared publication
Latest Publications
- Open Access
- 1 January 2013
- Published by American Institute of Mathematical Sciences (AIMS) in Communications on Pure and Applied Analysis
- Vol. 12 (1) , 237-252
The point-wise estimates of solutions for semi-linear dissipativewave equation
In this paper we focus on the global-in-time existence and the point-wise estimates of solutions to the initial value problem for the semi-linear dissipative wave equation in multi-dimensions. By using the method of Green function combined with the energy estimates, we obtain the point-wise decay estimates of solutions to the problem.
- 1 January 2013
- Published by American Institute of Mathematical Sciences (AIMS) in Communications on Pure and Applied Analysis
- Vol. 12 (1) , 237-252
Open AccessThe point-wise estimates of solutions for semi-linear dissipativewave equation
In this paper we focus on the global-in-time existence and the point-wise estimates of solutions to the initial value problem for the semi-linear dissipative wave equation in multi-dimensions. By using the method of Green function combined with the energy estimates, we obtain the point-wise decay estimates of solutions to the problem.
- Open Access
- 1 January 2011
- Published by American Institute of Mathematical Sciences (AIMS) in Kinetic and Related Models
- Vol. 4 (2) , 531-547
Decay property for a plate equation with memory-type dissipation
In this paper we focus on the initial value problem of the semi-linear plate equation with memory in multi-dimensions $(n\geq1)$, the decay structure of which is of regularity-loss property. By using Fourier transform and Laplace transform, we obtain the fundamental solutions and thus the solution to the corresponding linear problem. Appealing to the point-wise estimate in the Fourier space of solutions to the linear problem, we get estimates and properties of solution operators, by exploiting which decay estimates of solutions to the linear problem are obtained. Also by introducing a set of time-weighted Sobolev spaces and using the contraction mapping theorem, we obtain the global in-time existence and the optimal decay estimates of solutions to the semi-linear problem under smallness assumption on the initial data.- 1 January 2011
- Published by American Institute of Mathematical Sciences (AIMS) in Kinetic and Related Models
- Vol. 4 (2) , 531-547
Open AccessDecay property for a plate equation with memory-type dissipation
In this paper we focus on the initial value problem of the semi-linear plate equation with memory in multi-dimensions $(n\geq1)$, the decay structure of which is of regularity-loss property. By using Fourier transform and Laplace transform, we obtain the fundamental solutions and thus the solution to the corresponding linear problem. Appealing to the point-wise estimate in the Fourier space of solutions to the linear problem, we get estimates and properties of solution operators, by exploiting which decay estimates of solutions to the linear problem are obtained. Also by introducing a set of time-weighted Sobolev spaces and using the contraction mapping theorem, we obtain the global in-time existence and the optimal decay estimates of solutions to the semi-linear problem under smallness assumption on the initial data. - Open Access
- 1 January 2011
- Published by American Institute of Mathematical Sciences (AIMS) in Communications on Pure and Applied Analysis
- Vol. 10 (1) , 209-223
Asymptotic behavior of solutions to a model system of a radiating gas
In this paper we focus on the initial value problem for a hyperbolic-elliptic coupled system of a radiating gas in multi-dimensional space. By using a time-weighted energy method, we obtain the global existence and optimal decay estimates of solutions. Moreover, we show that the solution is asymptotic to the linear diffusion wave which is given in terms of the heat kernel.
- 1 January 2011
- Published by American Institute of Mathematical Sciences (AIMS) in Communications on Pure and Applied Analysis
- Vol. 10 (1) , 209-223
Open AccessAsymptotic behavior of solutions to a model system of a radiating gas
In this paper we focus on the initial value problem for a hyperbolic-elliptic coupled system of a radiating gas in multi-dimensional space. By using a time-weighted energy method, we obtain the global existence and optimal decay estimates of solutions. Moreover, we show that the solution is asymptotic to the linear diffusion wave which is given in terms of the heat kernel.
- Open Access
- 1 January 2011
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 30 (3) , 1113-1139
Global existence and asymptotic behaviorof solutions for quasi-linear dissipative plate equation
In this paper we focus on the initial value problem for quasi-linear dissipative plate equation in multi-dimensional space $(n\geq2)$. This equation verifies the decay property of the regularity-loss type, which causes the difficulty in deriving the global a priori estimates of solutions. We overcome this difficulty by employing a time-weighted $L^2$ energy method which makes use of the integrability of $||$(∂$^2_xu_t,$∂$^3_xu)(t)||_{L^{\infty}}$. This $L^\infty$ norm can be controlled by showing the optimal $L^2$ decay estimates for lower-order derivatives of solutions. Thus we obtain the desired a priori estimate which enables us to prove the global existence and asymptotic decay of solutions under smallness and enough regularity assumptions on the initial data. Moreover, we show that the solution can be approximated by a simple-looking function, which is given explicitly in terms of the fundamental solution of a fourth-order linear parabolic equation.- 1 January 2011
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 30 (3) , 1113-1139
Open AccessGlobal existence and asymptotic behaviorof solutions for quasi-linear dissipative plate equation
In this paper we focus on the initial value problem for quasi-linear dissipative plate equation in multi-dimensional space $(n\geq2)$. This equation verifies the decay property of the regularity-loss type, which causes the difficulty in deriving the global a priori estimates of solutions. We overcome this difficulty by employing a time-weighted $L^2$ energy method which makes use of the integrability of $||$(∂$^2_xu_t,$∂$^3_xu)(t)||_{L^{\infty}}$. This $L^\infty$ norm can be controlled by showing the optimal $L^2$ decay estimates for lower-order derivatives of solutions. Thus we obtain the desired a priori estimate which enables us to prove the global existence and asymptotic decay of solutions under smallness and enough regularity assumptions on the initial data. Moreover, we show that the solution can be approximated by a simple-looking function, which is given explicitly in terms of the fundamental solution of a fourth-order linear parabolic equation. - Open Access
Asymptotic Behavior of Solutions to a Model System of a Radiating Gas
In this paper we focus on the initial value problem for a hyperbolic-elliptic coupled system of a radiating gas in multi-dimensional space. By using a time-weighted energy method, we obtain the global existence and optimal decay estimates of solutions. Moreover, we show that the solution is asymptotic to the linear diffusion wave which is given in terms of the heat kernel.
Open AccessAsymptotic Behavior of Solutions to a Model System of a Radiating Gas
In this paper we focus on the initial value problem for a hyperbolic-elliptic coupled system of a radiating gas in multi-dimensional space. By using a time-weighted energy method, we obtain the global existence and optimal decay estimates of solutions. Moreover, we show that the solution is asymptotic to the linear diffusion wave which is given in terms of the heat kernel.
- Open Access
Global Existence and Asymptotic Behavior of Solutions for Quasi-linear Dissipative Plate Equation
In this paper we focus on the initial value problem for quasi-linear dissipative plate equation in multi-dimensional space $(n\geq2)$. This equation verifies the decay property of the regularity-loss type, which causes the difficulty in deriving the global a priori estimates of solutions. We overcome this difficulty by employing a time-weighted $L^2$ energy method which makes use of the integrability of $\|(\p^2_xu_t,\p^3_xu)(t)\|_{L^{\infty}}$. This $L^\infty$ norm can be controlled by showing the optimal $L^2$ decay estimates for lower-order derivatives of solutions. Thus we obtain the desired a priori estimate which enables us to prove the global existence and asymptotic decay of solutions under smallness and enough regularity assumptions on the initial data. Moreover, we show that the solution can be approximated by a simple-looking function, which is given explicitly in terms of the fundamental solution of a fourth-order linear parabolic equation.Open AccessGlobal Existence and Asymptotic Behavior of Solutions for Quasi-linear Dissipative Plate Equation
In this paper we focus on the initial value problem for quasi-linear dissipative plate equation in multi-dimensional space $(n\geq2)$. This equation verifies the decay property of the regularity-loss type, which causes the difficulty in deriving the global a priori estimates of solutions. We overcome this difficulty by employing a time-weighted $L^2$ energy method which makes use of the integrability of $\|(\p^2_xu_t,\p^3_xu)(t)\|_{L^{\infty}}$. This $L^\infty$ norm can be controlled by showing the optimal $L^2$ decay estimates for lower-order derivatives of solutions. Thus we obtain the desired a priori estimate which enables us to prove the global existence and asymptotic decay of solutions under smallness and enough regularity assumptions on the initial data. Moreover, we show that the solution can be approximated by a simple-looking function, which is given explicitly in terms of the fundamental solution of a fourth-order linear parabolic equation. - Open Access
The Pointwise Estimates of Solutions for Semilinear Dissipative Wave Equation
In this paper we focus on the global-in-time existence and the pointwise estimates of solutions to the initial value problem for the semilinear dissipative wave equation in multi-dimensions. By using the method of Green function combined with the energy estimates, we obtain the pointwise estimates of the solution.
Open AccessThe Pointwise Estimates of Solutions for Semilinear Dissipative Wave Equation
In this paper we focus on the global-in-time existence and the pointwise estimates of solutions to the initial value problem for the semilinear dissipative wave equation in multi-dimensions. By using the method of Green function combined with the energy estimates, we obtain the pointwise estimates of the solution.
- 1 November 2008
- Published by Elsevier in Journal of Differential Equations
- Vol. 245 (9) , 2477-2503
Well-posedness of the IBVP for 2-D Euler equations with damping
- 1 November 2008
- Published by Elsevier in Journal of Differential Equations
- Vol. 245 (9) , 2477-2503
Well-posedness of the IBVP for 2-D Euler equations with damping
- Open Access$L^p-L^q$ estimates on the solutions to $u_{tt}-u_{x_1x_1}=\triangle u_t$This paper focuses the study on the $L^p-L^q$ estimates on the solutions to an asymmetric wave equation with dissipation which arises in the study for the magneto-hydrodynamics by using the method of Green function.Open Access$L^p-L^q$ estimates on the solutions to $u_{tt}-u_{x_1x_1}=\triangle u_t$This paper focuses the study on the $L^p-L^q$ estimates on the solutions to an asymmetric wave equation with dissipation which arises in the study for the magneto-hydrodynamics by using the method of Green function.
- Open Access
Well-posedness of the IBVP for 2-D Euler Equations with Damping
In this paper we focus on the initial-boundary value problem of the 2-D isentropic Euler equations with damping. We prove the global-in-time existence of classical solution to the initial-boundary value problem by the method of energy estimates.
Open AccessWell-posedness of the IBVP for 2-D Euler Equations with Damping
In this paper we focus on the initial-boundary value problem of the 2-D isentropic Euler equations with damping. We prove the global-in-time existence of classical solution to the initial-boundary value problem by the method of energy estimates.