Atnaujinkite slapukų nuostatas

El. knyga: Nonlocal Diffusion Problems

, , ,
Kitos knygos pagal šią temą:
Nonlocal Diffusion ProblemsDidesnis paveikslėlis
Kitos knygos pagal šią temą:

DRM apribojimai

  • Kopijuoti:

    neleidžiama

  • Spausdinti:

    neleidžiama

  • El. knygos naudojimas:

    Skaitmeninių teisių valdymas (DRM)
    Leidykla pateikė šią knygą šifruota forma, o tai reiškia, kad norint ją atrakinti ir perskaityti reikia įdiegti nemokamą programinę įrangą. Norint skaityti šią el. knygą, turite susikurti Adobe ID . Daugiau informacijos  čia. El. knygą galima atsisiųsti į 6 įrenginius (vienas vartotojas su tuo pačiu Adobe ID).

    Reikalinga programinė įranga
    Norint skaityti šią el. knygą mobiliajame įrenginyje (telefone ar planšetiniame kompiuteryje), turite įdiegti šią nemokamą programėlę: PocketBook Reader (iOS / Android)

    Norint skaityti šią el. knygą asmeniniame arba „Mac“ kompiuteryje, Jums reikalinga  Adobe Digital Editions “ (tai nemokama programa, specialiai sukurta el. knygoms. Tai nėra tas pats, kas „Adobe Reader“, kurią tikriausiai jau turite savo kompiuteryje.)

    Negalite skaityti šios el. knygos naudodami „Amazon Kindle“.

Nonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems are also of great interest for their purely mathematical content. This book presents recent results on nonlocal evolution equations with different boundary conditions, starting with the linear theory and moving to nonlinear cases, including two nonlocal models for the evolution of sandpiles. Both existence and uniqueness of solutions are considered, as well as their asymptotic behaviour. Moreover, the authors present results concerning limits of solutions of the nonlocal equations as a rescaling parameter tends to zero. With these limit procedures the most frequently used diffusion models are recovered: the heat equation, the $p$-Laplacian evolution equation, the porous media equation, the total variation flow, a convection-diffusion equation and the local models for the evolution of sandpiles due to Aronsson-Evans-Wu and Prigozhin. Readers are assumed to be familiar with the basic concepts and techniques of functional analysis and partial differential equations. The text is otherwise self-contained, with the exposition emphasizing an intuitive understanding and results given with full proofs. It is suitable for graduate students or researchers. The authors cover a subject that has received a great deal of attention in recent years. The book is intended as a reference tool for a general audience in analysis and PDEs, including mathematicians, engineers, physicists, biologists, and others interested in nonlocal diffusion problems.

Recenzijos

The results of this book are given with complete proofs and also an emphasis on the intuitive understanding of the results. This extends the audience beyond mathematicians to include engineers, physicists and biologists with a good background in Analysis and PDEs. -- Mathematical Reviews

Preface xi
Chapter 1 The Cauchy problem for linear nonlocal diffusion
1(30)
1.1 The Cauchy problem
1(9)
1.1.1 Existence and uniqueness
5(1)
1.1.2 Asymptotic behaviour
6(4)
1.2 Refined asymptotics
10(12)
1.2.1 Refined asymptotics
10(7)
1.2.2 Asymptotics for the higher order terms
17(3)
1.2.3 A different approach
20(2)
1.3 Rescaling the kernel. A nonlocal approximation of the heat equation
22(1)
1.4 Higher order problems
23(8)
1.4.1 Existence and uniqueness
24(1)
1.4.2 Asymptotic behaviour
25(3)
1.4.3 Rescaling the kernel in a higher order problem
28(1)
Bibliographical notes
29(2)
Chapter 2 The Dirichlet problem for linear nonlocal diffusion
31(10)
2.1 The homogeneous Dirichlet problem
31(5)
2.1.1 Asymptotic behaviour
32(4)
2.2 The nonhomogeneous Dirichlet problem
36(5)
2.2.1 Existence, uniqueness and a comparison principle
36(2)
2.2.2 Convergence to the heat equation when rescaling the kernel
38(2)
Bibliographical notes
40(1)
Chapter 3 The Neumann problem for linear nonlocal diffusion
41(24)
3.1 The homogeneous Neumann problem
41(4)
3.1.1 Asymptotic behaviour
42(3)
3.2 The nonhomogeneous Neumann problem
45(20)
3.2.1 Existence and uniqueness
46(2)
3.2.2 Rescaling the kernels. Convergence to the heat equation
48(6)
3.2.3 Uniform convergence in the homogeneous case
54(2)
3.2.4 An L1-convergence result in the nonhomogeneous case
56(1)
3.2.5 A weak convergence result in the nonhomogeneous case
57(6)
Bibliographical notes
63(2)
Chapter 4 A nonlocal convection diffusion problem
65(34)
4.1 A nonlocal model with a nonsymmetric kernel
65(4)
4.2 The Linear semigroup revisited
69(7)
4.3 Existence and uniqueness of the convection problem
76(6)
4.4 Rescaling the kernels. Convergence to the local convection-diffusion problem
82(8)
4.5 Long time behaviour of the solutions
90(6)
4.6 Weakly nonlinear behaviour
96(3)
Bibliographical notes
98(1)
Chapter 5 The Neumann problem for a nonlocal nonlinear diffusion equation
99(24)
5.1 Existence and uniqueness of solutions
100(15)
5.1.1 Notation and preliminaries
100(4)
5.1.2 Mild solutions and contraction principle
104(8)
5.1.3 Existence of solutions
112(3)
5.2 Rescaling the kernel. Convergence to the local problem
115(7)
5.3 Asymptotic behaviour
122(1)
Bibliographical notes
122(1)
Chapter 6 Nonlocal p-Laplacian evolution problems
123(40)
6.1 The Neumann problem
124(18)
6.1.1 Existence and uniqueness
125(3)
6.1.2 A precompactness result
128(3)
6.1.3 Rescaling the kernel. Convergence to the local p-Laplacian
131(6)
6.1.4 A Poincare type inequality
137(4)
6.1.5 Asymptotic behaviour
141(1)
6.2 The Dirichlet problem
142(12)
6.2.1 A Poincare type inequality
144(2)
6.2.2 Existence and uniqueness of solutions
146(3)
6.2.3 Convergence to the local p-Laplacian
149(4)
6.2.4 Asymptotic behaviour
153(1)
6.3 The Cauchy problem
154(6)
6.3.1 Existence and uniqueness
154(3)
6.3.2 Convergence to the Cauchy problem for the local p-Laplacian
157(3)
6.4 Nonhomogeneous problems
160(3)
Bibliographical notes
161(2)
Chapter 7 The nonlocal total variation flow
163(28)
7.1 Notation and preliminaries
164(1)
7.2 The Neumann problem
165(10)
7.2.1 Existence and uniqueness
166(3)
7.2.2 Rescaling the kernel. Convergence to the total variation flow
169(5)
7.2.3 Asymptotic behaviour
174(1)
7.3 The Dirichlet problem
175(16)
7.3.1 Existence and uniqueness
176(4)
7.3.2 Convergence to the total variation flow
180(8)
7.3.3 Asymptotic behaviour
188(1)
Bibliographical notes
189(2)
Chapter 8 Nonlocal models for sandpiles
191(32)
8.1 A nonlocal version of the Aronsson-Evans-Wu model sandpiles
191(22)
8.1.1 The Aronsson-Evans-Wu model for sandpiles
191(2)
8.1.2 Limit as p → ∞ in the nonlocal p-Laplacian Cauchy problem
193(2)
8.1.3 Rescaling the kernel. Convergence to the local problem
195(2)
8.1.4 Collapse of the initial condition
197(3)
8.1.5 Explicit solutions
200(10)
8.1.6 A mass transport interpretation
210(2)
8.1.7 Neumann boundary conditions
212(1)
8.2 A nonlocal version of the Prigozhin model for sandpiles
213(10)
8.2.1 The Prigozhin model for sandpiles
214(1)
8.2.2 Limit as → +∞ in the nonlocal p-Laplacian Dirichlet problem
214(3)
8.2.3 Convergence to the Prigozhin model
217(2)
8.2.4 Explicit solutions
219(3)
Bibliographical notes
222(1)
Appendix A Nonlinear semigroups
223(26)
A.1 Introduction
223(1)
A.2 Abstract Cauchy problems
224(3)
A.3 Mild solutions
227(2)
A.4 Accretive operators
229(6)
A.5 Existence and uniqueness theorem
235(4)
A.6 Regularity of the mild solution
239(2)
A.7 Convergence of operators
241(1)
A.8 Completely accretive operators
242(7)
Bibliography 249(6)
Index 255
Daugiau apie elektronines knygas Daugiau apie elektronines knygas
Pastovi nuoroda: https://www.kriso.lt/db/97814704139272e.html
Raktažodžiai: