DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS

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GLOBAL CONVERGENT ALGORITHM FOR PARABOLIC COEFFICIENT INVERSE PROBLEMS QUAN-FANG WANG The globally convergent algorithm, that is, convexification approach will be applied to coefficient inverse problems of parabolic differential equations when spatial dimensions are two. Based on the unified framework of convexification approach, a developed global iteration scheme for solving numerical solution will be implemented to verify the effectiveness of convexification approach for 2D parabolic case. Copyright © 2006 Quan-Fang Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction Global convergent algorithm is to solve the multidimensional coefficient inverse problems both in theoretical and computation issues using a unified framework (cf. [6]). Its application to a class of inverse problems has been reported in literatures (cf. [1–7]). The main thoughts of convexification approach focus on several aspects. Comparing the local convergent iteration to exact solution, convexification approach is a global convergent algorithm, which avoids leading to false solution under incomplete boundary data and inconsistency of a mathematical model with the reality. A couple of points clearly show its advantages. The sequential minimization algorithm (i) provides stable approximate solution via minimization of a finite sequence of strictly convex objective functions, which is constructed by applying the nonlinear weighted least-squares method with Carleman’s weight function; (ii) provides the convergence to the “exact” solution independent of starting vector, which is directly determined from the data eliminating for the descent methods. The purpose is to use convexification approach for solving the coefficient inverse problem arising in parabolic partial differential equations. Numerical study will be implemented for two dimensions to show the effectiveness. The contents of this paper are as follows. In Section 2, the formulation is given in the unified framework of convexification approach. In Section 3, the global convergent algorithm is applied to parabolic coefficient inverse problems. In Section 4, experiments Hindawi Publishing Corporation Proceedings of the Conference on Differential & Difference Equations and Applications, pp. 1109–1119
MULTIPLE POSITIVE RADIAL SOLUTIONS FOR QUASILINEAR EQUATIONS IN ANNULAR DOMAINS HAIYAN WANG We study the number of positive radial solutions of elliptic equations when nonlinearity has zeros. We show that the problem has k positive solutions if the nonlinearity has k zeros. Similar results are also true for elliptic systems. Copyright © 2006 Haiyan Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction In this paper we consider the multiplicity of positive radial solutions for the quasilinear equations div ( A ( |∇u| ) ∇u ) + λb ( |x| ) f (u) = 0 inD, u = 0 forx ∈ ∂D, div ( A ( |∇u| ) ∇u ) ( ) + λb 1 |x| g1 (u,v) = 0 inD, div ( A ( |∇v| ) ∇v ) ( ) + λb 2 |x| g2 (u,v) = 0 inD, u = v = 0 forx ∈ ∂D, (1.1) (1.2) where D ={x : x ∈ R n , n ≥ 2, 0 1, Hindawi Publishing Corporation Proceedings of the Conference on Differential & Difference Equations and Applications, pp. 1121–1130
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Proceedings of the Conference on Di
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Proceedings of the Conference on Di
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CONTENTS Preface...................
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Inequalities for positive solutions
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Modelling the effect of surgical st
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Maximum principles for elliptic equ
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A UNIFIED APPROACH TO MONOTONE METH
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IMPULSIVE CONTROL OF THE POPULATION
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BOUNDARY ESTIMATES FOR BLOW-UP SOLU
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SECOND-ORDER DIFFERENTIAL GRADIENT
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ON STRUCTURE OF FRACTIONAL SPACES G
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ON THE STABILITY OF THE DIFFERENCE
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TWO-WEIGHTED POINCARÉ-TYPE INTEGRA
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PRODUCT DIFFERENCE EQUATIONS APPROX
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QUASIDIFFUSION MODEL OF POPULATION
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FIXED-SIGN EIGENFUNCTIONS OF TWO-PO
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MULTIPLE POSITIVE SOLUTIONS OF SUPE
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SPECTRAL STABILITY OF ELLIPTIC SELF
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HO CHARACTERISTIC EQUATIONS SURPASS
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ASYMPTOTIC STABILITY IN DISCRETE MO
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CONTINUOUS AND DISCRETE NONLINEAR I
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ON PARABOLIC SYSTEMS WITH DISCONTIN
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INEQUALITIES FOR POSITIVE SOLUTIONS
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NONOSCILLATION OF ONE OF THE COMPON
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ANNULAR JET AND COAXIAL JET FLOW JO
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JUSTIFICATION OF QUADRATURE-DIFFERE
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VLASOV-ENSKOG EQUATION WITH THERMAL
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SUBDIFFERENTIAL OPERATOR APPROACH T
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A DISCRETE EIGENFUNCTIONS METHOD FO
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ON NONLINEAR SCHRÖDINGER EQUATIONS
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NUMERICAL SOLUTION OF A TRANSMISSIO
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THE SEMILINEAR EVOLUTION EQUATION F
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ON DOUBLY PERIODIC SOLUTIONS OF QUA
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DYNAMICS OF A DISCONTINUOUS PIECEWI
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PROBABILISTIC SOLUTIONS OF THE DIRI
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MONOTONICITY RESULTS AND INEQUALITI
Page 76 and 77: WELL-POSEDNESS AND BLOW-UP OF SOLUT
Page 78 and 79: REARRANGEMENT ON THE UNIT BALL FOR
Page 80 and 81: CONVERGENCE OF SERIES OF TRANSLATIO
Page 82 and 83: ON MINIMAL (MAXIMAL) COMMON FIXED P
Page 84 and 85: BOUNDEDNESS OF SOLUTIONS OF FUNCTIO
Page 86 and 87: MODELLING THE EFFECT OF SURGICAL ST
Page 88 and 89: LIMIT CYCLES OF LIÉNARD SYSTEMS M.
Page 90 and 91: MAXIMUM PRINCIPLES AND DECAY ESTIMA
Page 92 and 93: LIPSCHITZ REGULARITY OF VISCOSITY S
Page 94 and 95: ON AN ELASTIC BEAM FULLY EQUATION W
Page 96 and 97: BOUNDARY VALUE PROBLEMS ON THE HALF
Page 98 and 99: EXISTENCE AND UNIQUENESS OF AN INTE
Page 100 and 101: STABILITY OF SOME MODELS OF CIRCULA
Page 102 and 103: LIPSCHITZ CLASSES OF A-HARMONIC FUN
Page 104 and 105: A TWO-DEGREES-OF-FREEDOM HAMILTONIA
Page 106 and 107: QUANTIZATION OF LIGHT FIELD IN PERI
Page 108 and 109: CONSERVATION LAWS IN QUANTUM SUPER
Page 110 and 111: ON SETS OF ZERO HAUSDORFF s-DIMENSI
Page 112 and 113: ON THE GLOBAL ATTRACTOR IN A CLASS
Page 114 and 115: SANDWICH PAIRS MARTIN SCHECHTER Sin
Page 116 and 117: EXISTENCE RESULTS FOR EVOLUTION INC
Page 118 and 119: AVERAGING DOMAINS: FROM EUCLIDEAN S
Page 120 and 121: CONCENTRATION-COMPACTNESS PRINCIPLE
Page 122 and 123: NONLINEAR VARIATIONAL INCLUSION PRO
Page 124 and 125: MAXIMUM PRINCIPLES FOR ELLIPTIC EQU
Page 128 and 129: SECOND-ORDER NONLINEAR OSCILLATIONS
Page 130 and 131: ANALYTIC SOLUTIONS OF UNSTEADY CRYS
Page 132 and 133: UNBOUNDEDNESS OF SOLUTIONS OF PLANA
Page 134 and 135: QUENCHING OF SOLUTIONS OF NONLINEAR
Page 136 and 137: VARIATION-OF-PARAMETERS FORMULAE AN
Page 138: DIFFERENCE EQUATIONS AND THE ELABOR
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DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS

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