Nonlinear evolution equations with a fractional derivative on a half-line

被引：2
作者：
Kaikina, Elena I. [1 ]
机构：
[1] Univ Nacl Autonoma Mexico, Inst Matemat, Morelia 58089, Michoacan, Mexico
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 3-4期
关键词：
Dissipative nonlinear evolution equation; Large time asymptotics; Fractional derivative; LARGE TIME BEHAVIOR; SEMILINEAR PARABOLIC EQUATION; VISCOUS CONSERVATION-LAWS; BURGERS-EQUATION; CRITICAL EXPONENTS; WAVES; ASYMPTOTICS; STABILITY;
D O I：
10.1016/j.na.2008.10.106
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the initial-boundary value problem on a half-line for the nonlinear evolution equations with a fractional derivative. We study traditionally important problems of a theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time. (C) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码：766 / 781
页数：16
相关论文
共 35 条
[21]   HYPERBOLIC SYSTEMS OF CONSERVATION LAWS .2. [J].
LAX, PD .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1957, 10 (04) :537-566
[22]  
Lions J. L., 1972, NONHOMOGENEOUS BOUND
[23]  
LIU TP, 1985, MEM AM MATH SOC, V56, P1
[24]   Behaviors of solutions for the Burgers equation with boundary corresponding to rarefaction waves [J].
Liu, TP ;
Matsumura, A ;
Nishihara, K .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1998, 29 (02) :293-308
[25]   ASYMPTOTICS TOWARD THE RAREFACTION WAVE OF THE SOLUTIONS OF BURGERS-EQUATION WITH NONLINEAR DEGENERATE VISCOSITY [J].
MATSUMURA, A ;
NISHIHARRA, K .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 23 (05) :605-614
[26]   ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR SCALAR VISCOUS CONSERVATION-LAWS WITH NONCONVEX NONLINEARITY [J].
MATSUMURA, A ;
NISHIHARA, K .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 165 (01) :83-96
[27]  
Matsumura A., 1986, Jpn. J. Appl. Math, V3, P1, DOI DOI 10.1007/BF03167088
[28]   Critical exponents for the blow-up of solutions with sign changes in a semilinear parabolic equation [J].
Mizoguchi, N ;
Yanagida, E .
MATHEMATISCHE ANNALEN, 1997, 307 (04) :663-675
[29]   Critical exponents for the decay rate of solutions in a semilinear parabolic equation [J].
Mizoguchi, N ;
Yanagida, E .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1998, 145 (04) :331-342
[30]  
NAKAO H, 2004, N HOLLAND MATH STUDI, V194, P319
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