CONNECTING ORBITS IN HILBERT SPACES AND APPLICATIONS TO PDE

被引：7

作者：

Smyrnelis, Panayotis ^{[1
]}

机构：

[1] Polish Acad Sci, Inst Math, PL-00656 Warsaw, Poland

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2020年 / 19卷 / 05期

关键词：

heteroclinic orbits; Hilbert spaces; bistable potentials; heteroclinic double layers; second and fourth order systems of PDE; STATIONARY LAYERED SOLUTIONS; SINGULAR PERTURBATION; MINIMIZERS; SYSTEM;

D O I：

10.3934/cpaa.2020122

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a general theorem on the existence of heteroclinic orbits in Hilbert spaces, and present a method to reduce the solutions of some P.D.E. problems to such orbits. In our first application, we give a new proof in a slightly more general setting of the heteroclinic double layers (initially constructed by Schatzman [20]), since this result is particularly relevant for phase transition systems. In our second application, we obtain a solution of a fouth order P.D.E. satisfying similar boundary conditions.

引用

页码：2797 / 2818

页数：22

共 50 条

[21] Semigroups, Potential Spaces and Applications to (S)PDE
Hinz, Michael
Zahle, Martina
POTENTIAL ANALYSIS, 2012, 36 (03) : 483 - 515
[22] Learning in Reproducing Kernel Hilbert Spaces for Orbits of Iterated Function Systems
Roy, Priyanka
Saminger-Platz, Susanne
COMBINING, MODELLING AND ANALYZING IMPRECISION, RANDOMNESS AND DEPENDENCE, SMPS 2024, 2024, 1458 : 413 - 420
[23] Monotonicity and existence of periodic orbits for projected dynamical systems on Hilbert spaces
Cojocaru, MG
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 134 (03) : 793 - 804
[24] AUGMENTED LAGRANGIAN AND PROXIMAL ALTERNATING DIRECTION METHODS OF MULTIPLIERS IN HILBERT SPACES. APPLICATIONS TO GAMES, PDE'S AND CONTROL
Attouch, H.
Soueycatt, M.
PACIFIC JOURNAL OF OPTIMIZATION, 2009, 5 (01): : 17 - 37
[25] Perron's method and the method of relaxed limits for "unbounded" PDE in Hilbert spaces
Kelome, Djivede
Swiech, Andrzej
STUDIA MATHEMATICA, 2006, 176 (03) : 249 - 277
[26] The Conley index in Hilbert spaces and its applications
Geba, K
Izydorek, M
Pruszko, A
STUDIA MATHEMATICA, 1999, 134 (03) : 217 - 233
[27] Functional inequalities on abstract Hilbert spaces and applications
Feng-Yu Wang
Mathematische Zeitschrift, 2004, 246 : 359 - 371
[28] APPLICATIONS OF FIXED POINT THEORY IN HILBERT SPACES
Dewangan, Kiran
KOREAN JOURNAL OF MATHEMATICS, 2024, 32 (01): : 59 - 72
[29] Functional inequalities on abstract Hilbert spaces and applications
Wang, FY
MATHEMATISCHE ZEITSCHRIFT, 2004, 246 (1-2) : 359 - 371
[30] SEQUENCES OF HILBERT SPACES WITH APPLICATIONS TO QUANTUM MECHANICS
BREITENECKER, M
GRUMM, HR
ACTA PHYSICA AUSTRIACA, 1971, 34 (1-2): : 1 - +

← 1 2 3 4 5 →