The second initial-boundary value problem for a quasilinear parabolic equations with nonlinear boundary conditions

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆａｓｔｄｉｆｆｕｓｉｏｎｅｑｕａｔｉｏｎｏｆｄｉｖｅｒｇｅｎｃｅｆｏｒｍａｓｕｔ =(ａ(ｕ)ｕｘ) ｘ ｂ(ｕ) ｘ ｃ(ｕ)　　 (ａ( 0 ) = ∞ ) ( 1 )ｈａｓｉｍｐｏｒｔａｎｔｐｈｙｓｉｃａｌｂａｃｋｇｒｏｕｎｄ ,ｓｕｃｈａｓ [1 ] .Ｉｎｒｅｃｅｎｔｙｅａｒｓ ,ｓｏｍｅｒｅｓｕｌｔｓａｂｏｕｔ ( 1 )ｈａｖｅｂｅｅｎｏｂｔａｉｎｅｄ .Ｆｏｒｅｘａｍｐｌｅ ,[2 ] ,[3]ｒｅｓｐｅｃｔｉｖｅｌｙｄｉｓｃｕｓｓｅｄｔｈｅＣａｕｃｈｙｐｒｏｂｌｅｍｓｆｏｒｅｑｕａｔｉｏｎ( 1 )ａｎｄｕｔ=(…     

The existence of periodic solutions of impulsive differential equations of mixed type

1　ＰｒｏｂｌｅｍｉｎｔｈｅＲｅｓｅａｒｃｈｏｆＴｏｒｏｉｄＩｍｐｕｌｓｉｖｅｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｉｓａｎｅｗｉｍｐｏｒｔａｎｔｂｒａｎｃｈｏｆｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ.Ｉｎ1989,[1],[2]ｓｙｓｔｅｍａｔｉｃａｌｌｙｓｕｍｍａｒｉｚｅｄｒｅｓｅａｒｃｈｗｏｒｋａｂｏｕｔｉｍｐｕｌｓｉｖｅｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ.Ｉｎｒｅｃｅｎｔｙｅａｒｓ,ｔｈｅｒｅａｒｅｍａｎｙｌｉｔｅｒａｔｕｒｅｓｄｅａｌｉｎｇｗｉｔｈｔｈｅｏｓｃｉｌｌａｔｉｏ…     

Fifth-order isotropic descartes tensor

Ｉｎｔｈｉｓｌｉｔｅｒａｔｕｒｅ [1 ] ,[2 ]ｏｒｄｅｒ 0～ 4ｉｓｏｔｒｏｐｉｃｄｅｓｃａｒｔｅｓｔｅｎｓｏｒ’ｓｅｘｉｓｔｅｎｃｅａｎｄｉｔｓｇｅｎｅｒａｌｒｅｐｒｅｓｅｎｔａｔｉｏｎｆｏｒｍｕｌａａｒｅｄｉｓｃｕｓｓｅｄ .Ｗｉｔｈｒｅｇａｒｄｔｏｏｒｄｅｒｋ ≥ 5(ｄｅｓｃａｒｔｅｓｔｅｎｓｏｒｏｒａｆｆｉｎｅｏｒｔｈｏｇｏｎａｌｔｅｎｓｏｒ) ,ｔｈｅｎｕｍｂｅｒ (3 ｋ)ｏｆｉｔｓｃｏｍｐｏｎｅｎｔｓｉｓｖｅｒｙｂｉｇ ,ａｎｄｉｔｓｓｔｒｕｃｔｕｒｅｉｓｖｅｒｙｃｏｍｐｌｉｃａｔｅｄ ,ｓｏｎｏｐａ…     

A family of integrable systems of Liouville and lax representation,Darboux transformations for its constrained flows

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｗｅｌｌ＿ｋｎｏｗｎｂａｓｉｓｏｆｌｏｏｐａｌｇｅｂｒａ Ａ1ｉｓｔｈａｔｈ(ｎ) =λｎ 　 00 -λｎ ,　ｅ(ｎ) =0λｎ0 0 ,ｆ(ｎ) =0 0λｎ 0 ,[ｈ(ｍ) ,ｅ(ｎ) ] =2ｅ(ｍ+ｎ) ,[ｈ(ｍ) ,ｆ(ｎ) ] =　　 -2ｆ(ｍ+ｎ) ,[ｅ(ｍ) ,ｆ(ｎ) ] =ｈ(ｍ+ｎ) .( 1 )Ｍａｎｙｅｑｕａｔｉｏｎｈｉｅｒａｒｃｈｉｅｓｗｅｒｅｏｂｔａｉｎｅｄｂｙｅｓｔａｂｌｉｓｈｉｎｇｌｉｎｅａｒｉｓｏｓｐｅｃｔｒａｌｐｒｏｂｌｅｍｖｉａｔｈｅｕｓｅｏｆ( 1 ) ,ｓｕｃｈａｓＡＫＮＳｈｉｅｒａｒｃｈｙ ,ＫＮｈｉｅｒａ…     

Elxed Point Theorem of Composition g-Contraction Mapping and its Applications

ＩｎｔｒｏｄｕｃｔｉｏｎＭａｎｙｓｔｕｄｉｅｓｈａｖｅｂｅｅｎｄｏｎｅｏｎｃｏｎｔｒａｃｔｉｖｅｍａｐｐｉｎｇｓ,ｅ .ｇ .,Ｒｈｏａｄｅｓ[1]ｍａｄｅａｃｏｍｐａｒｉｓｏｎｏｆｖａｒｉｏｕｓｄｅｆｉｎｉｔｉｏｎｓ (ｍｏｒｅｔｈａｎ 1 0 0ｔｙｐｅｓｖａｒｉｅｄｆｒｏｍ 2 5ｂａｓｉｃｔｙｐｅｓ)ｏｆｃｏｎｔｒａｃｔｉｖｅｍａｐｐｉｎｇｏｎｃｏｍｐｌｅｔｅｍｅｔｒｉｃｓｐａｃｅｉｎ 1 977.Ａｎｄｕｐｔｏｎｏｗ ,ｓｕｃｈｓｔｕｄｙｉｓｓｔｉｌｌｇｏｉｎｇｏｎ ,ｅ .ｇ .,[2 ] .Ｉｎｔｈｉｓｐａｐｅｒ,ｔｈｅｓｅ…     

Anomalous dynamics response of nonlinear elastic bar

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｓｅｎｔｙｅａｒｓ,ｔｈｅｃｈａｏｔｉｃｂｅｈａｖｉｏｒｏｆｂｅａｍｓｓｕｂｊｅｃｔｅｄｔｏｐｅｒｉｏｄｉｃｌｏａｄｂｒｉｎｇｓｍｏｒｅａｎｄｍｏｒｅｓｃｈｏｌａｒｓ’ｉｎｔｅｒｅｓｔｓ.Ｉｎ 1 983 ,ＦＣＭｏｏｎｅｔａｌ.[1]ｓｔｕｄｉｅｄｔｈｅｃｈａｏｔｉｃｍｏｔｉｏｎｓｏｆｂｅａｍｓｉｎｎｏｎｌｉｎｅａｒｂｏｕｎｄａｒｙｃｏｎｄｉｔｉｏｎｓ.Ｉｎ 1 994 ,Ｓ .ＡｎａｎｔｈａＲａｍｕａｎｄＴＳＳａｎｋａｒｅｔａｌ.[2 ]ａｎａｌｙｚｅｄｂｉｆｕｒｃａｔｉｏｎａｎｄＣａｔａ…     

THE TRANSIENT ELLIPTIC FLOW OF POWER-LAW FLUID IN FRACTAL POROUS MEDIA

1　ＴｈｅＦｌｏｗＭｏｄｅｌｏｆＰｏｗｅｒ＿ＬａｗＦｌｕｉｄｉｎＲａｄｉｃａｌＦｒａｃｔａｌＲｅｓｅｒｖｏｉｒＴｈｅｔｒａｎｓｉｅｎｔｆｌｏｗｏｆｐｏｗｅｒ＿ｌａｗｆｌｕｉｄｉｎｒａｄｉｃａｌｆｒａｃｔａｌｒｅｓｅｒｖｏｉｒｉｓｓｔｕｄｉｅｄｉｎＲｅｆ.[1 ] ,ａｎｄａｎａｌｙｔｉｃａｌｓｏｌｕｔｉｏｎｏｆＬａｐｌａｃｅｓｐａｃｅｉｓｄｅｒｉｖｅｄ .ＩｎＲｅｆ.[2 ] ,ｔｈｅｔｒａｎｓｉｅｎｔｅｌｌｉｐｔｉｃａｌｆｌｏｗｉｓｒｅｓｅａｒｃｈｅｄｏｎｍｏｄｅｌｏｆｅｘｐａｎｄｉｎｇｒｅｃｔａｎｇｌｅ .Ｔ…     

PRELIMINARY ANALYSIS OF SKATING MOTION

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｌｅｉｇｈｐｒｏｂｌｅｍｉｓａｃｌａｓｓｉｃｏｎｅｉｎｎｏｎｈｏｌｏｎｏｍｉｃｄｙｎａｍｉｃｓ.ＴｈｅｓｏｌｕｔｉｏｎｓｔｏｔｈｅｐｒｏｂｌｅｍｗｅｒｅｏｂｔａｉｎｅｄｂｙС .А .Чаплыгин( 1 898)ａｎｄＣ .Ｃａｒａｔｈｏｄｏｒｙ( 1 93 3 ) [1].Ｔｈｅｒｅｆｅｒｅｎｃｅ [2 ]ｐｒｅｓｅｎｔｅｄａｆｅｗｑｕｅｓｔｉｏｎａｂｌｅｐｏｉｎｔｓｉｎｔｈｅｓｏｌｕｔｉｏｎｓ .Ａｎｏｔｈｅｒｓｏｌｕｔｉｏｎｗａｓｏｆｆｅｒｅｄｉｎｔｈｅｒｅｆｅｒｅｎｃｅ[3 ] .Ｂｕｔｔｈｅ…     

Local attractors for weakly damped forced KdV equation in thin 2D domains

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓｍｕｃｈｐｒｏｇｒｅｓｓｈａｓｂｅｅｎｍａｄｅｏｎｔｈｅｈｉｇｈｅｒａｎｄｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓ (ｓｅｅ ,ｅ .ｇ .[1 ]～ [1 0 ] ) ,ａｎｄｍａｉｎｌｙｂａｓｅｄｏｎｒｅａｃｔｉｏｎ＿ｄｉｆｆｕｓｉｏｎｅｑｕａｔｉｏｎｓ,Ｋｕｒａｍｏｔｏ＿ＳｉｖａｓｈｉｎｓｋｙｅｑｕａｔｉｏｎｓＮａｖｉｅｒ＿Ｓｔｏｋｅｓｅｑｕａｔｉｏｎｓ ,ｅｔｃ .Ｂｅｃａｕｓｅｏｆｔｈｅｆａｃｔｔｈａｔｔｈｅｐｒｉｎｃｉｐａｌｏｐｅｒ…     

On very rotund banach space

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ [1 ] ,Ｆ .Ｓｕｌｌｉｖａｎｄｅｆｉｎｅｄｔｈｅｖｅｒｙｒｏｔｕｎｄｓｐａｃｅ ,ｗｈｉｃｈｉｓｔｈｅｄｕａｌｎｏｔｉｏｎｏｆｖｅｒｙｓｍｏｏｔｈｓｐａｃｅ.Ｉｎ [2 ] ,ｔｈｅｗｅａｋｌｙｅｘｐｏｓｅｄｐｏｉｎｔｗａｓｉｎｔｒｏｄｕｃｅｄ ,ｗｈｉｃｈｉｓａｇｅｎｅｒａｌｉｚａｔｉｏｎｏｆｔｈｅｓｔｒｏｎｇｌｙｅｘｐｏｓｅｄｐｏｉｎｔ.Ｉｔｉｓｋｎｏｗｎｔｈａｔｔｈｅｒｅｉｓａｃｌｏｓｅｄｃｏｎｎｅｃｔｉｏｎｂｅｔｗｅｅｎｔｈｅｓｔｒｏｎｇｌｙｅｘｐｏｓｅｄｐｏｉｎｔｓａｎｄ…     

A NOTE ON STOCHASTIC OPTIMAL CONTROL OF REFLECTED DIFFUSIONS WITH JUMPS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔｏｃｈａｓｔｉｃｏｐｔｉｍａｌｃｏｎｔｒｏｌｐｒｏｂｌｅｍｓｏｆｒｅｆｌｅｃｔｅｄｄｉｆｆｕｓｉｏｎｐｒｏｃｅｓｓｅｓｈａｓｂｅｅｎｃｏｎｓｉｄｅｒｅｄｂｙｓｏｍｅｍａｔｈｅｍａｔｉｃｉａｎｓ,ｆｏｒｉｎｓｔａｎｃｅ ,Ｐ .Ｌ .Ｌｉｏｎｓｉｎ [1 ] ,ａｎｄＪ.Ｌ .ＭｅｎａｌｄｉａｎｄＭ .Ｒｏｂｉｎｉｎ[2 ] .Ｉｎｔｈｉｓｐａｐｅｒ,ｗｅｗｉｌｌｃｏｎｓｉｄｅｒａｓｔｏｃｈａｓｔｉｃｏｐｔｉｍａｌｃｏｎｔｒｏｌｐｒｏｂｌｅｍｏｆｒｅｆｌｅｃｔｅｄｄｉｆｆｕｓｉｏｎｓｗｉｔ…     

BLOW-UP OF THE SOLUTIONS FOR THE INITIAL-BOUNDARY PROBLEMS OF THE NONLINEAR SCHR?DINGER EQUATIONS

Ｔｈｅｒｅａｒｅｍａｎｙｄｏｃｕｍｅｎｔｓｔｈａｔｄｉｓｃｕｓｓｂｌｏｗ＿ｕｐｏｆｔｈｅｓｏｌｕｔｉｏｎｓｆｏｒｔｈｅｉｎｉｔｉａｌ＿ｂｏｕｎｄａｒｙｖｌｕｅｐｒｏｂｌｅｍｓｏｆｔｈｅｎｏｎｌｉｎｅａｒＳｃｈｒ ｄｉｎｇｅｒｅｑｕａｔｉｏｎｓ,ｓｕｃｈａｓｐａｐｅｒ [1 ] .Ｂｕｔｔｈｅｐａｐｅｒ [1 ]ｈａｓｏｎｅｗｅａｋｐｏｉｎｔ,ｔｈａｔｉｓ,ｉｔｃａｎｎｏｔｕｎｉｔｅｄｉｓｃｕｓｓｉｏｎｆｏｒｂｌｏｗ＿ｕｐｏｆｔｈｅｓｏｌｕｔｉｏｎｓｆｏｒｔｈｅｉｎｉｔｉａｌ＿ｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌ…     

Semi-inverse method and generalized variational principles with multi-variables in elasticity

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 1 954,Ｈｕ[1,2 ]ｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅｂｙｓｏ＿ｃａｌｌｅｄｔｒｉａｌ＿ａｎｄ＿ｅｒｒｏｒｍｅｔｈｏｄ ,ａｎｄｉｎ1 964 ,Ｃｈｉｅｎ[3]ｓｙｓｔｅｍａｔｉｃａｌｌｙｄｉｓｃｕｓｓｅｄｔｈｅＬａｇｒａｎｇｅｍｕｌｔｉｐｌｉｅｒｍｅｔｈｏｄ ,ｂｙｗｈｉｃｈｈｅｓｕｃｃｅｓｓｆｕｌｌｙｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅ.Ａｆｔｅｒｔｈａｔｇｅｎｅｒａｌｉｚｅｄｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅｓｃａｎｂｅａｒｒｉｖｅｄａｔ…     

Probability Inequalities for Sums of Independent Unbounded Random Variables

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔ Ｙｎ ｂｅａｓｅｑｕｅｎｃｅｏｆｉ.ｉ.ｄ .ｒａｎｄｏｍｖａｒｉａｂｌｅｓｏｎａｐｒｏｂａｂｉｌｉｔｙｓｐａｃｅ(Ω ,Ｔ ,Ｐ)ａｎｄｌｅｔＳｎ =∑ｎｉ=1Ｙｉ.Ｂｅｎｎｅｔｔ( 1 962 ) [1]ａｎｄＨｏｅｆｆｄｉｎｇ ( 1 963) [2 ]ｒｅｓｐｅｃｔｉｖｅｌｙｓｔｕｄｙｓｕｍｓｏｆｉｎｄｅｐｅｎｄｅｎｔｒａｎｄｏｍｖａｒｉａｂｌｅｓａｎｄｇｉｖｅｉｍｐｏｒｔａｎｔｐｒｏｂａｂｉｌｉｔｙｉｎｅｑｕａｌｉｔｉｅｓｕｎｄｅｒｔｈｅｃｏｎｄｉｔｉｏｎｗｈｉｃｈＹｉ,1 ≤ｉ≤ｎａｒｅｂｏｕｎｄ…     

Element functions of discrete operator difference method

ＩｎｔｒｏｄｕｃｔｉｏｎＤｉｓｃｒｅｔｅｏｐｅｒａｔｏｒｗａｓｐｕｓｈｅｄｆｏｒｗａｒｄｉｎｐａｐｅｒｓ [1 ,2 ] ,ｗｈｉｃｈｔｒｉｅｄｔｏｕｎｉｆｙｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄａｎｄｄｉｆｆｅｒｅｎｃｅｍｅｔｈｏｄｉｎｔｏｏｎｅｕｎｉｆｏｒｍｆｒａｍｅａｎｄｂｅｎｅｆｉｔｕｓｆｏｒｆｉｎｄｉｎｇｎｅｗｍｅｔｈｏｄｓ.ＰｒｏｆｅｓｓｏｒＬＩＲｏｎｇ＿ｈｕａｅｔａｌ.ｇａｖｅａｍｅｔｈｏｄ‘ｇｅｎｅｒａｔｅｄｉｆｆｅｒｅｎｃｅｍｅｔｈｏｄ’[3,4 ]ｉｓａｋｉｎｄｏｆｉｎｎｏｖａｔｉｏｎａｎｄｄ…     

The effects of blood viscoelasticity on the pulse wave in arteries

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈａｔｔｈｅｂｌｏｏｄｈａｓｖｉｓｃｏｅｌａｓｔｉｃｐｒｏｐｅｒｔｉｅｓｉｓａｗｅｌｌ＿ｋｎｏｗｎｆａｃｔ.ＴｈｅｒｅｓｅａｒｃｈｅｓｆｏｒｔｈｅｂｌｏｏｄｖｉｓｃｏｅｌａｓｔｉｃｉｔｙｂｙＧ .Ｂ .Ｔｈｕｒｓｔｏｎ[1～4]ａｎｄＳ .Ｃｈｉｅｎ[5 ]ｓｈｏｗｔｈａｔｔｈｅｂｌｏｏｄｎｏｔｏｎｌｙａｐｐｅａｒｓｔｈｅｖｉｓｃｏｅｌａｓｔｉｃｉｔｙｉｎｖａｒｉｏｕｓｏｓｃｉｌｌａｔｏｒｙｂｌｏｏｄｆｌｏｗｓ,ｂｕｔａｌｓｏｈａｓｑｕｉｔｅｓｔｒｏｎｇｅｌａｓｔｉｃｉｔｙｉｎｓｏｍｅ…     

One-Dimensional Consolidation of Layered and Visco-Elastic Soils under Arbitrary Loading

ＩｎｔｒｏｄｕｃｔｉｏｎＡｆｔｅｒＴｅｒｚａｇｈｉ,ａｌｏｔｏｆｓｃｈｏｌａｒｓｈａｖｅｄｏｎｅｏｕｔｓｔａｎｄｉｎｇｒｅｓｅａｒｃｈｏｎｔｈｅｐｒｏｂｌｅｍｓｏｆｏｎｅ＿ｄｉｍｅｎｓｉｏｎａｌｃｏｎｓｏｌｉｄａｔｉｏｎ .Ｗｉｌｓｏｎ ( 1974) [1] ａｎｄＢａｌｉｇｈ( 1978) [2 ] ｅｔａｌ.ｈａｖｅｓｔｕｄｉｅｄｔｈｅｃｏｎｓｏｌｉｄａｔｉｏｎｕｎｄｅｒｔｈｅｒｅｃｔａｎｇｕｌａｒｌｏａｄｉｎｇ .Ｉｎ 1988,ＷＵｅｔａｌ.[3] ｗｏｒｋｅｄｏｕｔｔｈｅｇｅｎｅｒａｌｓｏｌｕｔｉｏｎｓｏｆｏｎｅ＿ｄｉｍｅｎ…     

The research of blow-up in 2D weakly damped forced KdV equation on thin domain

ＩｎｔｒｏｄｕｃｔｉｏｎＷｉｔｈｃｏｍｐｌｅｘｉｔｙｏｆｔｈｅｄｙｎａｍｉｃｓｏｆｔｈｅｈｉｇｈｅｒ＿ｄｉｍｅｎｓｉｏｎａｌｄｉｓｓｉｐａｔｉｖｅｓｙｓｔｅｍｓｏｌｉｔａｒｙｗａｖｅ ,ｔｈｅｒｅｉｓｍｕｃｈｄｉｆｆｉｃｕｌｔｙｉｎｓｔｕｄｙｉｎｇｔｈｅｓｅｐｒｏｂｌｅｍｓ.Ｔｈｅｐａｐｅｒｓ [1 ]～ [3]ｍｅｎｔｉｏｎｅｄｔｈｅｔｗｏ＿ｄｉｍｅｎｓｉｏｎａｌＫｄＶｅｑｕａｔｉｏｎｓｄｒｉｖｅｎｂｙＬａｘａｎｄ [3]ｏｂｔａｉｎｅｄｔｈｅｅｘｉｓｔｅｎｃｅｏｆｓｏｌｕｔｉｏｎｔｏｔｈｅｅｑｕａｔｉｏｎｓ…     

EXPONENTIAL STABILITY OF INTERVAL DYNAMICAL SYSTEM WITH MULTIDELAY

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔａｂｉｌｉｔｙｏｆｔｈｅｉｎｔｅｒｖａｌｍａｔｒｉｘａｎｄｕｎｃｅｒｔａｉｎｓｙｓｔｅｍｗｉｔｈｔｉｍｅｄｅｌａｙｈａｖｅｂｅｅｎｃｏｎｓｉｄｅｒｅｄｂｙｒｅｓｅａｒｃｈｅｒｓｉｎｔｈｅｐａｐｅｒｓ [1 -1 3 ] .Ｔｈｅｓｔａｂｉｌｉｔｙａｎｄαｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙｏｆｔｈｅｆｏｌｌｏｗｉｎｇｉｎｔｅｒｖａｌｄｙｎａｍｉｃａｌｓｙｓｔｅｍｗｉｔｈｓｉｎｇｌｅｔｉｍｅｄｅｌａｙ ｘ(ｔ) =Ｎ[Ｐ ,Ｑ]ｘ(ｔ) +Ｎ[Ｃ ,Ｄ]ｘ(ｔ-τ)ｈａｖｅｂｅｅｎｃｏｎｓｉ…     

CONVERGENCE OF SIMPLIFIED AND STABILIZED MIXED ELEMENT FORMATS BASED ON BUBBLE FUNCTION FOR THE STOKES PROBLEM

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｏｒｄｅｒｔｏｇｅｔｒｉｄｏｆｔｈｅｒｅｓｔｒｉｃｔｉｏｎｔｏｄｉｓｃｒｅｔｅＢａｂｕｓｋａ＿Ｂｒｅｚｚｉ’ｓｃｏｎｄｉｔｉｏｎｓｉｎｒｅｓｅａｒｃｈｅｓｏｆｍｉｘｅｄｆｉｎｉｔｅｅｌｅｍｅｎｔ (ＭＦＥ)ｍｅｔｈｏｄｓ,ｏｎｅｕｓｕａｌｌｙｕｓｅｓｔｈｅｓｔａｂｉｌｉｚｅｄＭＦＥｍｅｔｈｏｄｓｆｏｒｍａｔ[1] .Ｔｈｅｒｅａｒｅａｎｕｍｂｅｒｏｆｓｔａｂｉｌｉｚｅｄｍｅｔｈｏｄｓ (ｓｅｅ ,ｅ.ｇ .,Ｒｅｆｓ.[1- 7]ａｎｄｔｈｅｒｅｆｅｒｅｎｃｅｓｔｈｅｒｅｉｎ) ,ｗｈｉｃｈｈ…