Michel Chipot

l Goes to Plus Infinity (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book provides proofs of the asymptotic behavior of solutions to various important cases of linear and nonlinear problems in the theory of elliptic and parabolic partial differential equations. It is a valuable resource for graduates and researchers in applied mathematics and for engineers. Many results presented here have not been published elsewhere. They will motivate and enable the reader to apply the theory to other problems in partial differential equations.

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Produktdetails

• Verlag: Birkhäuser Basel
• Seitenzahl: 181
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783034881739
• Artikelnr.: 53164139

Autorenporträt

Chipot, M., University of Zurich, Switzerland

Inhaltsangabe

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.- 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.- 4. Nonlinear Elliptic Problems.- 4.1. Variational inequalities.- 4.2. Quasilinear elliptic problems.- 4.3. Strongly nonlinear problems.- 5. Asymptotic Behaviour of some Nonlinear Elliptic Problems.- 5.1. The case of variational inequalities.- 5.2. The case of quasilinear problems.- 6. Elliptic Systems.- 6.1. Some inequalities.- 6.2. Existence results for linear elliptic systems.- 6.3. Nonlinear elliptic systems.- 7. Asymptotic Behaviour of Elliptic Systems.- 7.1. The case of linear elliptic systems satisfying the Legendre condition.- 7.2. The system of elasticity.- 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.- Concluding Remark.