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quasilinear MODEL IN PHARMACOKINETICS

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Chinese Science Bulletin 1991年第20期36卷 1746-1750页

作者：丁勇 Department of Biomathematics Nanjing Medical College Nanjing 210029 PRC

In classical linear pharmacokinetics, elimination rate of drugs is regarded as a constant, so elimination of drugs is independent of dose. But recent studies have showed that it is not true for some drugs. Levy found in 1965 that the elimination of salicylamide is dosedependent and its biological half-life increases with dose. To account for this phenomenon,

关键词： quasilinear model elimination rate dose heparin.

LIFE-SPAN OF CLASSICAL SOLUTIONSTO quasilinear HYPERBOLIC SYSTEMSWITH SLOW DECAY INITIAL DATALIFE-SPAN OF CLASSICAL SOLUTIONSTO quasilinear HYPERBOLIC SYSTEMSWITH SLOW DECAY INITIAL DATA

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Chinese Annals of Mathematics,Series B 2000年第4期21卷 413-440页

作者： DEXING KONG Department of Applied Mathematics Shanghai Jiaotong University Shanghai 200030 China

The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1–1.3 in [2] are still valid for this kind of initial data.

关键词： quasilinear strictly hyperbolic system Weak linear degeneracy Cauchy problem Classical solution Life-span

Finite difference method of first boundary problem for quasilinear parabolic systems ( Ⅳ)——Convergence of iteration

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Science China Mathematics 1997年第11期40卷 469-474页

作者：周毓麟沈隆钧袁光伟 Institute of Applied Physics and Computational Mathematics Beijing 100088 China

More work is done to study the explicit, weak and strong implicit difference solution for the first boundary problem of quasilinear parabolic system:where u, , and f are m-dimensional vector valued functions, A is an m × m positively definite matrix, and ut = For this problem, the convergence of iteration for the general difference schemes is proved.

关键词： difference scheme quasilinear parabolic systems iteration.

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Science China Mathematics 2004年第5期47卷 659-674页

作者： SHI Peihu & WANG MingxinDepartment of Mathematics, Southeast University, Nanjing 210018, China Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, China Department of Mathematics Southeast University Nanjing China Department of Mathematics Xuzhou Normal University Xuzhou China

This paper is devoted to study the classification of self-similar solutions to the m ≥ 1,p,q ＞ 0 and p + q ＞ m. For m = 1, it is shown that the very singular self-similar solution exists if and only if nq + (n + 1)p ＜ n + 2, and in case of existence, such solution is unique. For m ＞ 1, it is shown that very singular self-similar solutions exist if and only if 1 ＜ m ＜ 2 and nq + (n + 1)p ＜ 2 + mn, and such solutions have compact support if they exist. Moreover, the interface relation is obtained.

关键词： quasilinear parabolic equations, self-similar solutions, very singular solution, classification.

THE SECOND INITIAL-BOUNDARY VALUE PROBLEM FOR A quasilinear PARABOLIC EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

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Applied Mathematics and Mechanics(English Edition) 2000年第11期21卷 1331-1337页

作者：潘佳庆 Department of Mathematics Jimei University Xiamen P R China

With prior estimate method, the existence, uniqueness, stability and large time behavior of the solution of second initial-boundary value problem for a fast diffusion equation with nonlinear boundary conditions are investigated. The main results are : 1) there exists only one global weak solution which continuously depends on initial value; 2) when t < T-0, the solution is infinitely continuously differentiable and is a classical solution; 3) the solution converges to zero uniformly as t is large enough.

关键词： fast-diffusion quasilinear nonlinear boundary conditions second initial-boundary value problem

Local Exact Boundary Synchronization for a Kind of First Order quasilinear Hyperbolic Systems

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Chinese Annals of Mathematics,Series B 2019年第1期40卷 79-96页

作者： Xing LU School of Mathematics Southeast University School of Mathematical Sciences Fudan University

In this paper, the synchronization for a kind of first order quasilinear hyperbolic system is taken into account. In this system, all the equations share the same positive wave speed. To realize the synchronization, a uniform constructive method is adopted, rather than an iteration process usually used in dealing with nonlinear systems. Furthermore,similar results on the exact boundary synchronization by groups can be obtained for a kind of first order quasilinear hyperbolic system of equations with different positive wave speeds by groups.

关键词： Exact boundary synchronization quasilinear hyperbolic system Exact boundary synchronization by groups

On a quasilinear elliptic eigenvalue problem with constraint

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Science China Mathematics 2004年第4期47卷 523-537页

作者： CHEN Jianqing CHEN Shaowei LI Yongqing Department of Mathematics Fujian Normal UniversityFuzhou 350007China Institute of Mathematics AMSSChinese Academy of SciencesBeijing 100080China

Via construction of pseudo gradient vector field and descending flow argument, we prove the existence of one positive, one negative and one sign-changing solutions for a quasilinear elliptic eigenvalue problem with co... 详细信息

关键词： multiple solutions, sign-changing solution, critical point theory, quasilinear elliptic eigenvalue.

DETERMINISTIC HOMOGENIZATION OF quasilinear DAMPED HYPERBOLIC EQUATIONS

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Acta Mathematica Scientia 2011年第5期31卷 1823-1850页

作者： Gabriel Nguetseng Hubert Nnang Nils Svanstedt Faculty of Sciences University of Yaounde I P.O. Box 812 Yaounde Cameroon Ecole Normale Suprieure University of Yaounde I P.O. Box 47 Yaounde Cameroon Department of Mathematical Sciences University of Gothenburg SE-412 96 Gteborg Sweden

Deterministic homogenization is studied for quasilinear monotone hyperbolic problems with a linear damping term. It is shown by the sigma-convergence method that the sequence of solutions to a class of multi-scale hig... 详细信息

关键词： homogenization sigma-convergence quasilinear hyperbolic

Asymptotical behavior of ground state solutions for critical quasilinear Schrodinger equation

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Frontiers of Mathematics in China 2020年第1期15卷 21-46页

作者： Yongpeng CHEN Yuxia GUO Zhongwei TANG School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China Department of Mathematics Tsinghua UniversityBeijing 100084China

This paper is concerned with the existence and asymptotical behavior of positive ground state solutions for a class of critical quasilinear Schrodinger *** using a change of variables and variational argument,we prove... 详细信息

关键词： quasilinear Schrodinger equation critical exponent ground state solution asymptotical behavior