Multiple-Scale Analysis of Boundary-Value Problems in Thick Multi-Level Junctions of Type 3:2:2 ()

Preface
Contents
1 Introduction
2 Homogenization of Linear Elliptic Problems
	2.1 Statement of Problems
	2.2 Auxiliary Statements and a Priori Estimates
		2.2.1 Auxiliary Statements
		2.2.2 A Priori Estimates
	2.3 Convergence Theorems
		2.3.1 Convergence Theorem for Problem (2.1)
		2.3.2 Convergence Theorem for Problem (2.2)
	2.4 Conclusions to this Chapter
3 Homogenization of Elliptic Problems  in Thick Junctions with Sharp Edges
	3.1 Statement of the Problem
	3.2 Auxiliary Statements
		3.2.1 Cases of Rounded and Linear Edges
		3.2.2 Case of Very Sharp Edges
		3.2.3 A Priori Estimate
		3.2.4 Weighted Sobolev Spaces
	3.3 Special Multivalued Extension
	3.4 Convergence Theorems
		3.4.1 The Case of Rounded Edges
		3.4.2 The Case of Wedge Edges
		3.4.3 The Case of Very Sharp Edges
	3.5 Conclusions to this Chapter
4 Homogenization of Semilinear Parabolic Problems
	4.1 Problem with Alternating Robin Boundary Conditions
		4.1.1 Statement of the Problem
		4.1.2 Auxiliary Statements
		4.1.3 Convergence Theorems
	4.2 Problem with Alternating Robin and Dirichlet Boundary Conditions
		4.2.1 Statement of the Problem
		4.2.2 Convergence Theorems
	4.3 Conclusions to this Chapter
5 Asymptotic Approximations  for Solutions to Semilinear Elliptic  and Parabolic Problems
	5.1 Semilinear Elliptic Problem
		5.1.1 Statement of the Problem
		5.1.2 Formal Asymptotic Expansions
		5.1.3 The Homogenized Problem
		5.1.4 Asymptotic Approximation and Estimates
	5.2 Semilinear Parabolic Problem
		5.2.1 Statement of the Problem
		5.2.2 Formal Asymptotic Expansions
		5.2.3 The Homogenized Problem
		5.2.4 Asymptotic Approximation and Estimates
	5.3 Conclusions to this Chapter
Appendix  References
Index