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l Goes to Plus Infinity




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Birkhäuser

Pubblicazione: 12/2001
Edizione: 2002





Trama

Many physical problems are meaningfully formulated in a cylindrical domain. When the size of the cylinder goes to infinity, the solutions, under certain symmetry conditions, are expected to be identical in every cross-section of the domain. The proof of this, however, is sometimes difficult and almost never given in the literature. The present book partially fills this gap by providing proofs of the asymptotic behaviour of solutions to various important cases of linear and nonlinear problems in the theory of elliptic and parabolic partial differential equations.
The book is a valuable resource for graduates and researchers in applied mathematics and for engineers. Many results presented here are original and have not been published elsewhere. They will motivate and enable the reader to apply the theory to other problems in partial differential equations.





Sommario

1. Introduction to Linear Elliptic Problems.- 1.1. The Lax—Milgram theorem.- 1.2. Elementary notions on Sobolev spaces.- 1.3. Applications to linear elliptic problems.- 2. Some Model Techniques.- 2.1. The case of lateral Dirichlet boundary conditions on a rectangle.- 2.2. The case of lateral Neumann boundary conditions on a rectangle.- 2.3. The case of lateral Dirichlet boundary conditions revisited.- 2.4. A different point of view.- Open problems.- 3. A General Asymptotic Theory for Linear Elliptic Problems.- 3.1. A general convergence result in H1 (S24,).- 3.2. A sharper rate of convergence.- 3.3. Convergence in higher Sobolev spaces.- Open problems.- 4. Nonlinear Elliptic Problems.- 4.1. Variational inequalities.- 4.2. Quasilinear elliptic problems.- 4.3. Strongly nonlinear problems.- Open problems.- 5. Asymptotic Behaviour of some Nonlinear Elliptic Problems.- 5.1. The case of variational inequalities.- 5.2. The case of quasilinear problems.- Open problems.- 6. Elliptic Systems.- 6.1. Some inequalities.- 6.2. Existence results for linear elliptic systems.- 6.3. Nonlinear elliptic systems.- Open problems.- 7. Asymptotic Behaviour of Elliptic Systems.- 7.1. The case of linear elliptic systems satisfying the Legendre condition.- 7.2. The system of elasticity.- Open problems.- 8. Parabolic Equations.- 8.1. Functional spaces for parabolic problems.- 8.2. Linear parabolic problems.- 8.3. Nonlinear parabolic problems.- 9. Asymptotic Behaviour of Parabolic Problems.- 9.1. The linear case.- 9.2. A nonlinear case.- Open problems.- Concluding Remark.










Altre Informazioni

ISBN:

9783764366469

Condizione: Nuovo
Collana: Birkhäuser Advanced Texts Basler Lehrbücher
Dimensioni: 235 x 155 mm Ø 1000 gr
Formato: Copertina rigida
Illustration Notes:VIII, 181 p.
Pagine Arabe: 181
Pagine Romane: viii


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