EXISTENCE RESULTS FOR A CLASS OF PSEUDOMONOTONE ELLIPTIC-PARABOLIC INCLUSIONS

doi:10.1016/S0252-9602(11)60355-X

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (5): 1709-1718.doi: 10.1016/S0252-9602(11)60355-X

EXISTENCE RESULTS FOR A CLASS OF PSEUDOMONOTONE ELLIPTIC-PARABOLIC INCLUSIONS

彭自嘉|刘益良^*

School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, China|Faculty of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, China

收稿日期:2010-09-02 出版日期:2011-09-20 发布日期:2011-09-20
通讯作者: 刘益良,yiliangliu100@126.com E-mail:pengzijia@126.com; yiliangliu100@126.com
基金资助:
Project supported by NSFC (10971019), Scientific Research Fund of Guangxi Education Department (201012MS067) and Hunan Provincial Innovation Foundation For Postgrad-uate (CX2010B117).

EXISTENCE RESULTS FOR A CLASS OF PSEUDOMONOTONE ELLIPTIC-PARABOLIC INCLUSIONS

PENG Zi-Jia, LIU Yi-Liang^*

School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, China|Faculty of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, China

Received:2010-09-02 Online:2011-09-20 Published:2011-09-20
Contact: LIU Yi-Liang,yiliangliu100@126.com E-mail:pengzijia@126.com; yiliangliu100@126.com
Supported by:
Project supported by NSFC (10971019), Scientific Research Fund of Guangxi Education Department (201012MS067) and Hunan Provincial Innovation Foundation For Postgrad-uate (CX2010B117).

摘要/Abstract

摘要：

This paper deals with the initial-value problem of nonlinear evolution inclu-sions of the form dB(u)/dt + A(u) ∋ f, v₀ ∈ B(u)(0), where the operator B is induced by a subgradient and A is pseudomonotone. Existence theorem is established via the time discretization technique and the regularization method. In contrast to the previous results, here we impose a weaker coerciveness condition on A and remove the strong monotonicity from B.

关键词: time-discretization, pseudomonotone operator, regularization

Abstract:

Key words: time-discretization, pseudomonotone operator, regularization

中图分类号:

35K15

彭自嘉, 刘益良. EXISTENCE RESULTS FOR A CLASS OF PSEUDOMONOTONE ELLIPTIC-PARABOLIC INCLUSIONS[J]. 数学物理学报(英文版), 2011, 31(5): 1709-1718.

PENG Zi-Jia, LIU Yi-Liang. EXISTENCE RESULTS FOR A CLASS OF PSEUDOMONOTONE ELLIPTIC-PARABOLIC INCLUSIONS[J]. Acta mathematica scientia,Series B, 2011, 31(5): 1709-1718.

参考文献

[1] Grange O, Mignot F. Sur la R´esolution d’une ´Equation et d’une In´equations Paraboliques non Lin´eaires. J Funct Anal, 1972, 11: 77–92

[2] DiBenedetto E. Showalter R E. Implicit degenerate evolution equations and applications. SIAM J Math Anal, 1981, 12: 731–751

[3] Akagi G. Doubly nonlinear evolution equations governed by time-dependent subdifferentials in reflexive Banach spaces. J Differ Equ, 2006, 231: 32–56

[4] Kubo M, Yamazaki N. Elliptic-parabolic variational inequalities with time-dependent contrains. Disc Conti Dyna Sys, 2007, 19: 335–359

[5] Kenmochi N, Pawlow I. A class of nonlinear elliptic-parabolic equations with time-dependent constrains. Nonlinear Analysis TMA, 1986, 10: 1181–1202

[6] Berm´udez A, Kurany J, Saguez C. An existence theorem for an implicit nonlinear evolution equation. Collect Math (Barcelona), 1984, 35: 19–34

[7] Maitre E, Witomski P. A pseudo-monotonicity adapted to doubly nonlinear elliptic-parabolic equations. Nonlinear Analysis, 2002, 50: 223–250

[8] Liu Z H. Periodic solutions for double degenerate quasilinear parabolic equations. Nonlinear Analysis TMA, 2002, 51(7): 1245–1257

[9] Liu Z H. Existence for implicit differential equations with nonmonotone perturbations. Israel J Math, 2002, 129: 363–372

[10] Liu Z H, Zhang S S. On the degree theory for multivalued (S+) type mappings. Appl Math Mech-English Edition, 1998, 19: 1141–1149

[11] Berkovits J, Mustonen V. Monotonicity methods for nonlinear evolution equations. Nonlinear Analysis TMA, 1996, 27: 1397–1405

[12] Carl S. Multiple solutions of quasilinear periodic-parabolic inclusions. Nonlinear Analysis, 2010, 72: 2909–2922

[13] Carl S, Motreanu D. Extremal solutions of quasilinear parabolic inclusions with generalized Clarke’s gra-dient. J Differ Equ, 2003, 191: 206–233

[14] Carl S, Motreanu D. Comparison principle for Quasilinear parabolic inclusions with Clarke’s gradient. Adv Nonl Stud, 2009, 9: 69-80

[15] Liu Z H. Existence results for quasilinear parabolic hemivariational inequalities. J Diff Eq, 2008, 244: 1395–1409

[16] Liu Z H. Browder-Tikhonov regularization of non-coercive evolution hemivariational inequalities. Inverse Problems, 2005, 21: 13–20

[17] Mig´orski S. On existence of solutions for parabolic hemivariational inequalities. J Compul Appl Math, 2001, 129: 77–87

[18] Ekland I, T´eman R. Convex Analysis and Variational Problems. Philadelphia: SIAM, 1999

[19] Zeidler E. Nonlinear Functional Analysis and Its Application, II(A & B). Berlin: Springer, 1990

[20] Simon J. Compact sets in the space Lp[0, T; B]. Annali di Math Pura ed Appl, 1987, 146: 65–96

[21] Zhou W S, Yao Z A. Cauchy problem for a degenerate parabolic equation with non-divergence form. Acta Math Sci, 2010, 30B(5): 1679–1686

EXISTENCE RESULTS FOR A CLASS OF PSEUDOMONOTONE ELLIPTIC-PARABOLIC INCLUSIONS

EXISTENCE RESULTS FOR A CLASS OF PSEUDOMONOTONE ELLIPTIC-PARABOLIC INCLUSIONS

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 14

Metrics

本文评价

推荐阅读 0

[1]	曹道珉, 彭双阶, 严树森. REGULARIZATION OF PLANAR VORTICES FOR THE INCOMPRESSIBLE FLOW[J]. 数学物理学报(英文版), 2018, 38(5): 1443-1467.
[2]	Santhosh GEORGE, C. D. SREEDEEP. LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES[J]. 数学物理学报(英文版), 2018, 38(1): 303-314.
[3]	Ioannis K. ARGYROS, Santhosh GEORGE. ITERATIVE REGULARIZATION METHODS FOR NONLINEAR ILL-POSED OPERATOR EQUATIONS WITH M-ACCRETIVE MAPPINGS IN BANACH SPACES[J]. 数学物理学报(英文版), 2015, 35(6): 1318-1324.
[4]	郭娟, 王金平. CONVERGENCE ANALYSIS OF THE LOPING OS-EM ITERATIVE VERSION OF THE CIRCULAR RADON TRANSFORM[J]. 数学物理学报(英文版), 2014, 34(6): 1875-1884.
[5]	杨帆, 傅初黎, 李晓晓. IDENTIFYING AN UNKNOWN SOURCE IN SPACE-FRACTIONAL DIFFUSION EQUATION[J]. 数学物理学报(英文版), 2014, 34(4): 1012-1024.
[6]	刘红, 宋永忠. ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM[J]. 数学物理学报(英文版), 2011, 31(2): 383-398.
[7]	黄小为, 吴传生, 吴笛. A FAST CONVERGENT METHOD OF ITERATED REGULARIZATION[J]. 数学物理学报(英文版), 2009, 29(2): 341-348.
[8]	王吉安; 李景; 刘振海. REGULARIZATION METHODS FOR NONLINEAR ILL-POSED PROBLEMS WITH ACCRETIVE OPERATORS[J]. 数学物理学报(英文版), 2008, 28(1): 141-150.
[9]	钟同德; 陈吕萍. THE PERMUTATION FORMULA OF SINGULAR INTEGRALS WITH BOCHNER-MARTINELLI KERNEL ON STEIN MANIFOLDS[J]. 数学物理学报(英文版), 2006, 26(4): 679-690.
[10]	曾三友, 丁立新, 康立山. A METHOD TO APPROACH OPTIMAL ESTORATION IN IMAGE RESTORATION ROBLEMS WITHOUT NOISE ENERGY NFORMATION[J]. 数学物理学报(英文版), 2003, 23(4): 512-.
[11]	田范基. GROWTH OF RANDOM DIRICHLET SERIES (I)[J]. 数学物理学报(英文版), 2000, 20(3): 390-396.
[12]	侯宗义, 杨宏奇. REGULARIZATION METHOD FOR IMPROVING OPTIMAL CONVERGENCE RATE OF THE REGULARIZED SOLUTION OF ILL-POSED PROBLEMS[J]. 数学物理学报(英文版), 1998, 18(2): 177-185.
[13]	陈宏. ON THE ASYMPTOTIC ORDER OF TIKHONOV REGULARIZATION WITH OPERATORS AND DATA ERROR[J]. 数学物理学报(英文版), 1998, 18(1): 35-44.
[14]	S. Abbasbandy, E. Babolian. AUTOMATIC AUGMENTED GALERKIN ALGORITHMS FOR FREDHOLM INTEGRAL EQUATIONS OF THE FIRST KIND[J]. 数学物理学报(英文版), 1997, 17(1): 69-84.