Class information for:
Level 1: KURAMOTO SIVASHINSKY EQUATION//INCREMENTAL UNKNOWNS//INERTIAL MANIFOLDS

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
14499 766 22.1 43%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
244 3       MATHEMATICS, APPLIED//MATHEMATICS//BLOW UP 46988
704 2             NAVIER STOKES EQUATIONS//GLOBAL ATTRACTOR//CAHN HILLIARD EQUATION 12952
14499 1                   KURAMOTO SIVASHINSKY EQUATION//INCREMENTAL UNKNOWNS//INERTIAL MANIFOLDS 766

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 KURAMOTO SIVASHINSKY EQUATION authKW 1276550 9% 46% 70
2 INCREMENTAL UNKNOWNS authKW 764307 3% 91% 21
3 INERTIAL MANIFOLDS authKW 657442 5% 45% 37
4 APPROXIMATE INERTIAL MANIFOLDS authKW 428739 3% 51% 21
5 NONLINEAR GALERKIN METHOD authKW 298950 2% 50% 15
6 CONTINUOUS DATA ASSIMILATION authKW 283461 1% 89% 8
7 DETERMINING MODES authKW 267953 1% 61% 11
8 DETERMINING NODES authKW 230624 1% 64% 9
9 VOLUME ELEMENTS AND NODES authKW 159448 1% 100% 4
10 LINEARLY IMPLICIT SCHEMES authKW 127557 1% 80% 4

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Mathematics, Applied 18623 61% 0% 470
2 Mathematics 5505 37% 0% 284
3 Physics, Mathematical 4138 21% 0% 160
4 Mechanics 601 11% 0% 81
5 Physics, Multidisciplinary 562 14% 0% 106
6 Mathematics, Interdisciplinary Applications 270 5% 0% 36
7 Physics, Fluids & Plasmas 171 4% 0% 32
8 Computer Science, Interdisciplinary Applications 46 3% 0% 21
9 Engineering, General 14 2% 0% 12
10 Computer Science, Software Engineering 6 1% 0% 9

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 10781 CONTROL DYNAM SYST 39862 0% 100% 1
2 ALL RUSSIAN SCI TECHNOL INFORMAT 39862 0% 100% 1
3 ANAL ECON METODOS CUANTITAT 39862 0% 100% 1
4 CMAF CIENCIAS 39862 0% 100% 1
5 EA 3590 39862 0% 100% 1
6 EQUIPE ANO 39862 0% 100% 1
7 FRE 2222 MATH PL 39862 0% 100% 1
8 LAM SP2MI 39862 0% 100% 1
9 MATEMAT LICADA COPUTAC 39862 0% 100% 1
10 MATH INFOMMT PLICAT LAMIA 39862 0% 100% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 PHYSICA D-NONLINEAR PHENOMENA 12118 6% 1% 44
2 NONLINEARITY 11003 4% 1% 30
3 RAIRO-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 7463 1% 3% 6
4 DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 5242 3% 1% 21
5 NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 4006 5% 0% 35
6 JOURNAL OF DIFFERENTIAL EQUATIONS 3706 3% 0% 26
7 PHYSICA D 3422 1% 1% 8
8 DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS 3230 1% 2% 4
9 JOURNAL OF NONLINEAR SCIENCE 3087 1% 1% 7
10 ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 3044 1% 1% 10

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 KURAMOTO SIVASHINSKY EQUATION 1276550 9% 46% 70 Search KURAMOTO+SIVASHINSKY+EQUATION Search KURAMOTO+SIVASHINSKY+EQUATION
2 INCREMENTAL UNKNOWNS 764307 3% 91% 21 Search INCREMENTAL+UNKNOWNS Search INCREMENTAL+UNKNOWNS
3 INERTIAL MANIFOLDS 657442 5% 45% 37 Search INERTIAL+MANIFOLDS Search INERTIAL+MANIFOLDS
4 APPROXIMATE INERTIAL MANIFOLDS 428739 3% 51% 21 Search APPROXIMATE+INERTIAL+MANIFOLDS Search APPROXIMATE+INERTIAL+MANIFOLDS
5 NONLINEAR GALERKIN METHOD 298950 2% 50% 15 Search NONLINEAR+GALERKIN+METHOD Search NONLINEAR+GALERKIN+METHOD
6 CONTINUOUS DATA ASSIMILATION 283461 1% 89% 8 Search CONTINUOUS+DATA+ASSIMILATION Search CONTINUOUS+DATA+ASSIMILATION
7 DETERMINING MODES 267953 1% 61% 11 Search DETERMINING+MODES Search DETERMINING+MODES
8 DETERMINING NODES 230624 1% 64% 9 Search DETERMINING+NODES Search DETERMINING+NODES
9 VOLUME ELEMENTS AND NODES 159448 1% 100% 4 Search VOLUME+ELEMENTS+AND+NODES Search VOLUME+ELEMENTS+AND+NODES
10 LINEARLY IMPLICIT SCHEMES 127557 1% 80% 4 Search LINEARLY+IMPLICIT+SCHEMES Search LINEARLY+IMPLICIT+SCHEMES

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 ROBINSON, JC , (1995) FINITE-DIMENSIONAL BEHAVIOR IN DISSIPATIVE PARTIAL-DIFFERENTIAL EQUATIONS.CHAOS. VOL. 5. ISSUE 1. P. 330-345 33 94% 29
2 FOIAS, C , MONDAINI, CF , TITI, ES , (2016) A DISCRETE DATA ASSIMILATION SCHEME FOR THE SOLUTION OF THE TWO-DIMENSIONAL NAVIER-STOKES EQUATION AND THEIR STAISTICS.SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS. VOL. 15. ISSUE 4. P. 2109 -2142 21 84% 0
3 YANG, AL , WU, YJ , HUANG, ZD , YUAN, JY , (2015) PRECONDITIONING ANALYSIS OF NONUNIFORM INCREMENTAL UNKNOWNS METHOD FOR TWO DIMENSIONAL ELLIPTIC PROBLEMS.APPLIED MATHEMATICAL MODELLING. VOL. 39. ISSUE 18. P. 5436 -5451 23 74% 0
4 DE MOURA, EP , ROBINSON, JC , (2014) LOG-LIPSCHITZ CONTINUITY OF THE VECTOR FIELD ON THE ATTRACTOR OF CERTAIN PARABOLIC EQUATIONS.DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS. VOL. 11. ISSUE 3. P. 211 -228 19 90% 0
5 FARHAT, A , LUNASIN, E , TITI, ES , (2016) ABRIDGED CONTINUOUS DATA ASSIMILATION FOR THE 2D NAVIER-STOKES EQUATIONS UTILIZING MEASUREMENTS OF ONLY ONE COMPONENT OF THE VELOCITY FIELD.JOURNAL OF MATHEMATICAL FLUID MECHANICS. VOL. 18. ISSUE 1. P. 1 -23 17 89% 1
6 JOLLY, MS , ROSA, R , TEMAM, R , (2001) ACCURATE COMPUTATIONS ON INERTIAL MANIFOLDS.SIAM JOURNAL ON SCIENTIFIC COMPUTING. VOL. 22. ISSUE 6. P. 2216-2238 27 87% 7
7 KALOGIROU, A , KEAVENY, EE , PAPAGEORGIOU, DT , (2015) AN IN-DEPTH NUMERICAL STUDY OF THE TWO-DIMENSIONAL KURAMOTO-SIVASHINSKY EQUATION.PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. VOL. 471. ISSUE 2179. P. - 23 68% 0
8 IOAKIM, X , SMYRLIS, YS , (2016) ANALYTICITY FOR KURAMOTO-SIVASHINSKY-TYPE EQUATIONS IN TWO SPATIAL DIMENSIONS.MATHEMATICAL METHODS IN THE APPLIED SCIENCES. VOL. 39. ISSUE 8. P. 2159 -2178 18 82% 0
9 AZOUANI, A , TITI, ES , (2014) FEEDBACK CONTROL OF NONLINEAR DISSIPATIVE SYSTEMS BY FINITE DETERMINING PARAMETERS - A REACTION-DIFFUSION PARADIGM.EVOLUTION EQUATIONS AND CONTROL THEORY. VOL. 3. ISSUE 4. P. 579 -594 17 89% 1
10 ZELIK, S , (2014) INERTIAL MANIFOLDS AND FINITE-DIMENSIONAL REDUCTION FOR DISSIPATIVE PDES.PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS. VOL. 144. ISSUE 6. P. 1245 -1327 21 68% 2

Classes with closest relation at Level 1


Rank Class id link
1 4698 PULLBACK ATTRACTOR//GLOBAL ATTRACTOR//RANDOM ATTRACTOR
2 12337 TWO LEVEL METHOD//NAVIER STOKES EQUATIONS//TWO GRID METHOD
3 30193 KCC THEORY//JACOBI STABILITY//VOLTERRA HAMILTON SYSTEMS
4 35132 STATISTICAL SOLUTION//EQUIP MODAL X//HOMOGENEOUS STATISTICAL SOLUTION
5 21774 THIN DOMAINS//CONCENTRATING TERMS//DUMBBELL DOMAINS
6 22480 APPROXIMATE DECONVOLUTION//NS ALPHA//SCOTT VOGELIUS ELEMENTS
7 26997 ATTRACTOR BIFURCATION//DYNAMIC TRANSITION THEORY//EXTENDED FISHER KOLMOGOROV EQUATION
8 15125 COMPLEX GINZBURG LANDAU EQUATION//GINZBURG LANDAU EQUATION//GENERALIZED GINZBURG LANDAU EQUATION
9 15111 PRIMITIVE EQUATIONS//SCI COMP PL MATH//PL MATH SCI COMP
10 12440 EXPONENTIAL DICHOTOMY//NONUNIFORM EXPONENTIAL DICHOTOMIES//UNIFORM EXPONENTIAL STABILITY

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