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Constanda C. (ed.), Potapenko S.S. (ed.) — Integral Methods in Science and Engineering: Techniques and Applications
Constanda C. (ed.), Potapenko S.S. (ed.) — Integral Methods in Science and Engineering: Techniques and Applications



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Название: Integral Methods in Science and Engineering: Techniques and Applications

Авторы: Constanda C. (ed.), Potapenko S.S. (ed.)

Аннотация:

The physical world is studied by means of mathematical models, which consist of differential, integral, and integro-differential equations accompanied by a large assortment of initial and boundary conditions. In certain circumstances, such models yield exact analytic solutions. When they do not, they are solved numerically by means of various approximation schemes. Whether analytic or numerical, these solutions share a common feature: they are constructed by means of the powerful tool of integration-the focus of this self-contained book.

An outgrowth of the Ninth International Conference on Integral Methods in Science and Engineering, this work illustrates the application of integral methods to diverse problems in mathematics, physics, biology, and engineering. The thirty two chapters of the book, written by scientists with established credentials in their fields, contain state-of-the-art information on current research in a variety of important practical disciplines. The problems examined arise in real-life processes and phenomena, and the solution techniques range from theoretical integral equations to finite and boundary elements.

Specific topics covered include spectral computations, atmospheric pollutant dispersion, vibration of drilling masts, bending of thermoelastic plates, homogenization, equilibria in nonlinear elasticity, modeling of syringomyelia, fractional diffusion equations, operators on Lipschitz domains, systems with concentrated masses, transmission problems, equilibrium shape of axisymmetric vesicles, boundary layer theory, and many more.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 298

Добавлена в каталог: 30.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
absolute discretization error      4
acceleration of spectral computations      9
adaptive Newton—Coates method      139
advection—diffusion—deposition model      27
anisotropic pseudodofferential operators      141
antiplane elasticity with microstructure      201
arithmetic of Taylor series      135
Asymptotic distribution of eigenvalues      259
atmospheric advection—diffusion equation      171
atmospheric pollutant dispersion      37
Atomic Force Microscope (AFM)      237
axisymmetric vesicles      267
Babuska—Brezzi condition      225
backward Kolmogoreov equation      289
Baker—Ericksen inequalities      112
Besov space      161
Bessel potential spaces      150
Betti numbers      163
Betti's reciprocal theorem      227
biconjugate gradient solver      239
Biot's equations      99
Biot's slow wave      100
Blatz—Ko material      196
boundary domain integral equations      150
Boundary element method      217
Boundary integral method      141
boundary integral operators      209
boundary moment-stress operator      64 76
boundary stress operator      84 202
Brakhage—Werner potentials      209
Bromwich inversion formula      50
canonical co-normal derivative      158
Caputo time derivative of fractional order      141
Cauchy strain tensor      100
Cauchy stress tensor      193
Cauchy's residue theorem      50
classical electrostatic problem      238
co-normal derivative operator      149
compressible elasticity      191
concentrated masses method      56
contact problem for a half space      228
contaminants in a turbulent flow      27
Controllability      261
convexity conditions in nonlinear elasticity      109
Coulombic interaction      238
crack in human bone      248
crack problem under stretching pressure      247
Dilatational wave      100
Direct method      75 86
Dirichlet boundary conditions      63 76 89 163 204 219 238
Dirichlet boundary value problem      83
dispersion relation      104
Displacement method      56
Divergence-free vector field      161
double GITT method      37
double iteration      14
Dynamic system      285
Eddy diffusivity      172
eigenfrequencies of drilling masts      55
Eigenvalue problem      9
Elastic foundation      83
elastic plate layer potentials      84
equations of motion for drilling masts      57
Equilibrium configuration      192
Euler—Bernoulli beam      257
Euler—Lagrange equations      109
Evolution problem      182
Extension operator      154
extensional motion of an elastic plate      83
exterior boundary value problems      220
Exterior Dirichlet problem      238
Falkner—Skan equation      277
fast numerical integration method      135
Fick theory      172
Finite element method      121
first Green identity      156
first-kind integral equations      127
Fox $H$-functions      141
Fractional diffusion equation      141
free vibrations of a drilling mast      58
Fundamental solution      141 142 209 219 239
Gaerding inequality      147
Galerkin approximation      3
Gaussian model      171
Gaussian quadrature      176
Gauss—Green formula      193
Generalized Integral Laplace Transform Technique (GILTT)      28
generalized integral transform technique (GITT)      37
Gevrey class semigroup      257
Green's formula      19 77
Hankel transformation      229
harmonic fine tractions      99
Harmonic oscillations      201
Heat potentials      19
Helmholtz equation      204 207
Helmholtz potential decomposition      99
Holomorphic mapping      67 77
homogenization in perforated domains      89
Image enhancement      127
Implicit Euler method      21
Indirect method      85
Integral equations      19
K-theory      27 171
Kahaner's test problem      139
Kantorovich—Krylov approximations      10
Korn's inequality      194
Lagrange multiplier method      272
Lamb's problem      99
Laplace transformation      47 65 76 145 172
Laplace-transformed boundary value problems      65 76
laser-induced melting      23
Linear stochastic system      286
Lipschitz boundary      93 183 218
Lipschitz domain      149 162 219
Lipschitz function      161
local eigenvalue problem      184
local minimizers      191
Lyapunov exponent      285
macroscopic stress tensor      100
Magnetic interaction      238
Markov process      286
matrix of fundamental solutions      68 84 249
Maxwell stress      240
Maxwell's equations      168
melting with spherical symmetry      17
microscale variable      90
Minimizing path      192
Mittag—Leffler functions      142
Mixed boundary value problems      227
mode shapes of drilling masts      55
modeling of syringomyelia      119
moment Lyapunov exponent      285
moment stability      285
Neumann boundary conditions      63 76 89 204 219
Neumann boundary value problem      248
Nondestructive testing      99
nonharmonic exponentials      261
nonlocal effects in turbulence closure      175
Nystroem method      21
parameter choice problem      127
Peclet number      174
Petrov—Galerkin scheme      220
Phase field      17
Piola stress tensor      192
plane asymmetric elasticity      247
planetary boundary layer (PBL)      27
Poincare inequality      94
Poincare—Steklov operator      79
Point collocation      239
Pointwise convergence      210
Poisson problem      163
poly convexity      110
poroelastic half space      99
Positive solutions      277
Principal symbol      145
principle of frame indifference      110
Projection methods      1
Quasiconvexity      110
quasimodes for spectral problems      181
radial equilibria      112
Radiation condition      203 207
Rank one convexity      110
real noise excitation      285
reciprocity in elastomechanics      227
Regularization      127
Rellich's lemma      205
Riesz basis property      257
rigid indentor      228
Sample stability      285
scale-invariance property      113
Second Green formula      157
shape equation      269
Shear wave      100
Single-layer potential      141 209
Singular integral      68
Singular integral equations      85
Sobolev space      65 83 86 141 149 163 192 218 249 259
Solid-liquid interface      19
solidification with spherical symmetry      17
Somigliana formula      78 86 250
spectral perturbation problem      183
spectral problems      181
spectral properties and control      257
sphere-plane capacitance system      240
stabilization of a four dimensional system      285
standing waves      181
stationary diffusion advection equation      37
Stellar atmospheres      1
Stiffness matrix      59 121
Stored-energy function      110
stretching of an isotropic cylinder      195
Strong ellipticity      110
Sturm—Liouville problem      37 260
super convergence      1
Sylvester equation      13
system iteration      127
Taylor series      135
Taylor statistical theory      41
temperature "moment"      64
Test functions      150
thermoelastic plate layer potentials      68
thermoelastic plate potential      68 79
thermoelastic plates      63
time-dependent bending of plates      63
time-dependent boundary integral equations      70
time-harmonic wave      207
Trace operator      67 77 143 150 161 249
Transfer equation      2
transient acoustic radiation      47
Transmission problems      207
Transverse vibrations of a beam      257
turbulent fluxes of contaminant      172
two-scale limits      90
two-sided estimates      191
uniform Hadamard inequality      193
uniqueness in nonlinear elasticity      109
van der Waal interaction      238
Variational problem      67 80 224
vibrating systems with concentrated masses      181
voids in the spinal cord      119
Volterra integral equations of the first kind      20
Wavelet bases      162
Weak solution      71 81 83 85 110
weakly singular integral operators      1 9
Yukawa's equation      219
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