Parabolic boundary value problems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1998
|
| Schriftenreihe: | Operator theory
101 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 285 - 295 |
| Beschreibung: | X, 298 S. |
| ISBN: | 3764329726 0817629726 |
Internformat
MARC
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| 100 | 1 | |a Ėjdelʹman, Samuil D. |d 1921- |e Verfasser |0 (DE-588)118030116 |4 aut | |
| 245 | 1 | 0 | |a Parabolic boundary value problems |c Samuil D. Eidelman ; Nicolae V. Zhitarashu. Transl. from the Russ. by Gennady Pasechnik und Andrei Iacob |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1998 | |
| 300 | |a X, 298 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator theory |v 101 | |
| 500 | |a Literaturverz. S. 285 - 295 | ||
| 650 | 7 | |a Problèmes aux limites |2 ram | |
| 650 | 7 | |a Équations différentielles paraboliques |2 ram | |
| 650 | 0 | 7 | |a Parabolisches Randwertproblem |0 (DE-588)4319434-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Parabolisches Randwertproblem |0 (DE-588)4319434-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Žitarašu, Nikolaj V. |e Verfasser |0 (DE-588)120629208 |4 aut | |
| 830 | 0 | |a Operator theory |v 101 |w (DE-604)BV000000970 |9 101 | |
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Datensatz im Suchindex
| _version_ | 1804126249559261184 |
|---|---|
| adam_text | Contents
Foreword xi
Chapter I
Equations and Problems 1
1.1 Equations 1
1.1.1 Introduction 1
1.1.2 Systems parabolic in the sense of Petrovskii 1
1.1.3 Systems parabolic in the sense of Solonnikov 4
1.2 Initial and boundary value problems 6
1.2.1 Introduction 6
1.2.2 The Cauchy problem. The initial value problem 8
1.2.3 Parabolic boundary value problems 10
1.2.4 Particular cases. Examples 16
1.2.5 Parabolic conjugation problems 21
1.2.6 Nonlocal parabolic boundary value problems 24
Chapter II
Functional Spaces 27
11.1 Spaces of test functions and distributions 27
II. 1.1 Definition and basic properties of distributions.
Spaces P(O) and V {Q) 27
II.1.2 Differentiation of distributions.
Multiplication of distributions by smooth functions 28
II. 1.3 Distributions with compact supports.
The spaces £(Q) and £ {Q), 5(fi) and S {Q) 28
II. 1.4 Convolution and direct product of distributions 29
II.l.5 Fourier and Laplace transformations of distributions 30
11.2 The Hilbert spaces H* and H* 32
11.2.1 The isotropic spaces H (R ) and H*+ (R ) 32
11.2.2 The isotropic spaces //S(R+) and their duals 33
11.2.3 Restriction to a hyperplane 34
11.2.4 The anisotropic Sobolev Slobodetskii spaces Ti 35
11.2.5 The anisotropic spaces W on R + 1. E l+X.
R^.1 and E% 36
vi Contents
11.2.6 The dual spaces Us 37
11.2.7 Traces and continuation of functions in
the anisotropic spaces 7ia 37
11.2.8 Weighted anisotropic spaces; basic properties 39
11.2.9 Embeddings, traces and continuation of functions
in weighted anisotropic spaces 40
11.2.10 Equivalent norms in Hs r(M.n+l~,), fts T(£ + 7),
Hs{Enri) 41
11.2.11 The spaces HS{G) and HS{T) 42
11.2.12 Thespaces HS{S+, /) andHs(n+,7) 43
II.3 Banach spaces of Holder functions 44
11.3.1 The spaces CS(G) and CS(T) 44
11.3.2 The spaces CS(T) and CS(S) 45
Chapter III
Linear Operators 47
111.1 Operators of potential type 47
111.2 Operators of multiplication by a function 50
111.2.1 Boundedness of truncation operators 50
111.2.2 Boundedness of the operators of multiplication
by smooth functions 52
111.3 Commutators. Green formulas 55
111.3.1 The operators Jn, Jo 55
111.3.2 Formulas for calculating V(x, D)v+{x) and
b(x ,t,D ,Dt)$ +{x t) 56
111.3.3 Formulas for calculating l{x,t,D, Dt )u++(x,t) 57
111.3.4 Corollaries. Commutation formulas for differential
and truncation operators. Green formulas 61
111.4 On equivalent norms in fts(E^+1,7), 7is(El+ j),
and Hs(Rl), s 0 63
111.4.1 Equivalents norms defined by truncations 63
111.4.2 Restriction of distributions to an open half space 66
111.5 The spaces Hs and W ^ 66
111.5.1 The spaces H(SK) (G) and H*^ (£++1,7) 67
111.5.2 The spaces ^KrP)(fi) and 71s{ktP)(Q+,7) 68
111.6 Differential operators in the space Ji 71
111.6.1 Definition of the operator lu in J7+; its boundedness 72
111.6.2 Definition of the operator lu g ; its boundedness 75
111.6.3 Definition of the operators lu ^, hi r; their boundedness .. 77
Contents vii
Chapter IV
Parabolic Boundary Value Problems in Half Space 79
IV.l Non homogeneous systems in the space W^+(Rn+1,7) 79
IV. 1.1 Non homogeneous systems in E+ 80
IV.1.2 Non homogeneous systems in Râ„¢ 81
IV.2 Initial value and Cauchy problems for parabolic systems
in spaces Hs 86
IV.2.1 Formulation of the initial value problem in
the spaces of distributions H 86
IV.2.2 The Cauchy problem in Ti. for a system
parabolic in in the sense of Petrovskii 89
IV.2.3 Theorem on the solvability of the general
initial value problem 97
IV.3 Model parabolic boundary value problems in R++ 98
IV.3.1 Formulation of^the model boundary value problem
in the spaces Hs for a system parabolic in the
sense of Petrovskii 98
IV.3.2 Reduction of the boundary value problem to a system
of linear algebraic equations 103
IV.3.3 Analysis of the algebraic system:
construction of a solution analytic in p 105
IV.3.4 Theorem on well posedness of the model parabolic
boundary value problem in the spaces Hs, s —tm + | ... 107
IV.3.5 Analysis of the model boundary value problem in H.
with data compatible with zero at t = 0 110
IV.3.6 Equivalence of Condition IV.l and
the Lopatinskii condition 121
IV.4 The model boundary value problem in R++ for
general parabolic systems 124
IV.4.1 Formulation of the boundary value problem 124
IV.4.2 The model boundary value problem with
data compatible with zero 128
IV.5 The model parabolic conjugation problem in
classes of smooth functions 130
IV.5.1 Formulation of the problem;
the compatible covering condition 130
IV.5.2 Reduction of the model conjugation problem to an equivalent
boundary value problem for a block diagonal system 132
viii Contents
IV.6 Boundary value problem in 7Y^(M + ,7) for operators in which the
coefficients of the highest order derivatives
are slowly varying functions 135
IV.7 Conjugation problem for operators in which
the coefficients of the highest order derivatives
are slowly varying 142
Chapter V
Parabolic Boundary Value Problems in Cylindrical Domains 151
V.I Boundary value problems in a semi infinite cylinder 151
V.I.I Formulation of the boundary value problem
in ns(n+, 7) 151
V.1.2 Boundary value problem in f2+ = G x [0, 00) with
the data compatible with zero at t = 0. Regularizer 153
V.I.3 Boundary value problem in Q+ in the general case 159
V.2 Nonlocal boundary value problems. Conjugation problems 162
V.2.1 Problem setting in classes of smooth functions.
Conditions on operators 162
V.2.2 The nonlocal boundary value problem in the spaces 7is ... 164
V.2.3 The nonlocal boundary value problem in H with
data compatible with zero at t = 0 166
V.2.4 The nonlocal boundary value problem in Q+
in the general case 169
V.2.5 Parabolic conjugation problems 169
V.3 Boundary value problems in cylindrical domains
of finite height 171
V.4 Solvability of the parabolic boundary value problems
for right hand sides with regular singularities 172
V.4.1 Anisotropic regularizations of divergent integrals 173
V.4.2 The main solvability theorem 174
V.5 Green formula, boundary and initial values of
weak generalized solutions 175
V.5.1 Preliminary considerations. Notation 175
V.5.2 The main theorem on boundary and initial values 176
V.5.3 Limit values of weak generalized solutions on
the boundary of the domain 178
Contents jx
Chapter VI
The Cauchy Problem and Parabolic Boundary Value Problems in
Spaces of Smooth Functions 181
VI.l Fundamental solutions of the Cauchy problem 181
VI.1.1 Introduction 181
VI.1.2 Systems with bounded coefficients 182
VI.1.3 Systems with growing coefficients 189
VI.1.4 Second order parabolic equations 193
VI. 1.5 Estimates for fundamental solutions of parabolic
systems in R +1 and elliptic systems generated
by parabolic systems 198
VI.2 The Cauchy problem 203
VI.2.1 Introduction 203
VI.2.2 Well posedness 203
VI.2.3 Existence of a solution for systems with
growing coefficients 209
VI.2.4 Uniqueness 211
VI.2.5 Initial values for solutions of parabolic systems.
Integral representation of solutions 213
VI.3 Schauder theory of parabolic boundary value problems 216
VI.3.1 Introduction 216
VI.3.2 The well posedness theorem 216
VI.3.3 On the proof of the well posedness theorem 218
VI.3.4 Solution of the model parabolic boundary
value problem 219
VI.3.5 Necessity of the parabolicity condition 223
VI.3.6 General boundary value problems.
Well posedness theorem 225
VI.4 Green functions 227
VI.4.1 Introduction 227
VI.4.2 Green functions. Homogeneous Green functions 228
VI.4.3 The Green function for conjugation problems 232
Chapter VII
Behaviour of Solutions of Parabolic Boundary Value Problems
for Large Values of Time 233
VII.l Asymptotic representations and stabilization of solutions
of model problems 233
VII. 1.1 Formulation of the problem 233
VII.l.2 Poisson kernels of an elliptic boundary value problem
with a parameter 234
x Contents
VII. 1.3 Asymptotic representation of Poisson kernels of
an elliptic boundary value problem with a parameter 237
VII. 1.4 Definition of the class of boundary functions
used here 244
VII. 1.5 Asymptotic representation of solutions 246
VII. 1.6 Necessary and sufficient conditions of stabilization 249
VII.1.7 The case of a single equation and of boundary data
whose mean values have a limit 251
VII. 1.8 The case of a single space variable 253
VII.1.9 Examples 254
VII.2 Tikhonov s problem 255
VII.2.1 Statement of the problem. Notation. Conditions 255
VII.2.2 Lemmas 257
VII.2.3 Study of the Poisson kernel 258
VII.2.4 Stabilization theorem 266
VII.2.5 Examples 268
VII.2.6 Necessity 272
VII.2.7 Discussion 277
VII.2.8 Heat and mass exchange equations 278
VII.2.9 A model equation of higher order 280
Comments 283
References 285
Index 297
|
| any_adam_object | 1 |
| author | Ėjdelʹman, Samuil D. 1921- Žitarašu, Nikolaj V. |
| author_GND | (DE-588)118030116 (DE-588)120629208 |
| author_facet | Ėjdelʹman, Samuil D. 1921- Žitarašu, Nikolaj V. |
| author_role | aut aut |
| author_sort | Ėjdelʹman, Samuil D. 1921- |
| author_variant | s d ė sd sdė n v ž nv nvž |
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| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011711685 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:14:27Z |
| institution | BVB |
| isbn | 3764329726 0817629726 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007898055 |
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| physical | X, 298 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Ėjdelʹman, Samuil D. 1921- Verfasser (DE-588)118030116 aut Parabolic boundary value problems Samuil D. Eidelman ; Nicolae V. Zhitarashu. Transl. from the Russ. by Gennady Pasechnik und Andrei Iacob Basel [u.a.] Birkhäuser 1998 X, 298 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 101 Literaturverz. S. 285 - 295 Problèmes aux limites ram Équations différentielles paraboliques ram Parabolisches Randwertproblem (DE-588)4319434-5 gnd rswk-swf Parabolisches Randwertproblem (DE-588)4319434-5 s DE-604 Žitarašu, Nikolaj V. Verfasser (DE-588)120629208 aut Operator theory 101 (DE-604)BV000000970 101 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007898055&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ėjdelʹman, Samuil D. 1921- Žitarašu, Nikolaj V. Parabolic boundary value problems Operator theory Problèmes aux limites ram Équations différentielles paraboliques ram Parabolisches Randwertproblem (DE-588)4319434-5 gnd |
| subject_GND | (DE-588)4319434-5 |
| title | Parabolic boundary value problems |
| title_auth | Parabolic boundary value problems |
| title_exact_search | Parabolic boundary value problems |
| title_full | Parabolic boundary value problems Samuil D. Eidelman ; Nicolae V. Zhitarashu. Transl. from the Russ. by Gennady Pasechnik und Andrei Iacob |
| title_fullStr | Parabolic boundary value problems Samuil D. Eidelman ; Nicolae V. Zhitarashu. Transl. from the Russ. by Gennady Pasechnik und Andrei Iacob |
| title_full_unstemmed | Parabolic boundary value problems Samuil D. Eidelman ; Nicolae V. Zhitarashu. Transl. from the Russ. by Gennady Pasechnik und Andrei Iacob |
| title_short | Parabolic boundary value problems |
| title_sort | parabolic boundary value problems |
| topic | Problèmes aux limites ram Équations différentielles paraboliques ram Parabolisches Randwertproblem (DE-588)4319434-5 gnd |
| topic_facet | Problèmes aux limites Équations différentielles paraboliques Parabolisches Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007898055&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
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