partial differential equation toolbox pdf

... turn the first page: What does this toolbox do? Can I use it? What problems can I solve?, etc What Does this Toolbox Do? The Partial Differential Equation (PDE) Toolbox provides a powerful and flexible ... Element Method The Elliptic Equation 4-3 The Elliptic System 4-10 The Parabolic Equation 4-13 The Hyperbolic Equation 4-16 The Eigenvalue Equation 4-17 Nonlinear Equations 4-21 Adaptive ... study and solution of partial differential equations in two space dimensions and time The equations are discretized by the Finite Element Method (FEM) The objectives of the PDE Toolbox are to provide

Ngày tải lên: 26/01/2014, 02:20

... [1-5] First-order abstract partial differential equations with impulses are treated in [6-9] The literature related to ordinary and partial functional differential equations with delay for which ... related to partial functional differential equations with state-dependent delay is limited, to our knowledge, to the recent works [21,22] The study of impulsive partial functional differential equations ... impulsive abstract partial functional differential equation with state-dependent delay (~) 2006 Elsevier Ltd All rights reserved K e y w o r d s - - A b s t r a c t functional differential equations,

Ngày tải lên: 29/10/2015, 14:19

... 8Stochastic Partial Differential Equation Models for Highway Traffic byGunnar Gunnarsson We introduce a new model for multi-lane highway traffic, based onstochastic partial differential equations ... Trang 1UNIVERSITY OF CALIFORNIASanta Barbara Stochastic Partial Differential Equation Models for Highway Traffic A Dissertation submitted in partial satisfaction of the requirement for the degree ... Committee Chairman Guillaume Bonnet, Committee Chairman September 2006 Trang 4Stochastic Partial Differential Equation Models for Highway TrafficCopyright c byGunnar Gunnarsson Trang 5To my family

Ngày tải lên: 23/05/2017, 22:15

... differential equations,” Electronic Journal of Differential Equations, vol 2006, pp 1–12, 2006 21 S Zhang, “The existence of a positive solution for a nonlinear fractional differential equation,” ... nonlinear fractional differential equations with integral boundary conditions The results are established by converting the problem into an equivalent integral equation and applying Krasnoselskii’s ... advantage of fractional differential equations in comparison with classical integer-order models An excellent account in the study of fractional differential equations can be found in 1–5 For the

Ngày tải lên: 21/06/2014, 16:20

... kinetic equations A Some physical PDE Trang 41 Compressible Euler equations2 Compressible Euler equations in one dimension a Computing entropy/entropy flux pairs VIII Probability and differential equations ... B Some general theories 1 Entropy and efficiency Trang 3IV Elliptic and parabolic equationsA Entropy and elliptic equations b Second derivatives in time c A differential form of Harnack’s inequality ... Trang 1Entropy and Partial Differential EquationsLawrence C Evans Department of Mathematics, UC Berkeley Inspiring Quotations

Ngày tải lên: 17/03/2014, 14:29

... Trang 1P AR TIAL DIFFERENTIAL EQUA TIONSBJÖRN E J DAHLBERGCARLOS E KENIGISSN 0347-2809 DEPARTMENT OF MATHEMATICSCHALMERS ... 8Dirichlet problem
Neumann problem 
@u @n =the clamped plate problem 
u +rdiv(ru +ruT)and Stoke's equation 3 Fredholm theory for Dirichlet problem for domain with C2 boundary We start with an example ... problem Dg(P) = Z @ @nQR(P;Q)g(Q)d(Q) P 2 ;where R(P;Q) is the fundamental solution for Laplace equation in R n+1 (multiplied with ?1) and g 2 L2( D for some choice of g we have the right behaviour

Ngày tải lên: 31/03/2014, 15:16

... 2 Regular Equations 128 3 Pseudoparabolic Equations 132 4 Degenerate Equations 136 5 Examples 138 VISecond Order Evolution Equations 145 1 Introduction 145 2 Regular Equations ... problemsfor partial dierential equations Chapters V and VI provide the immediateextensions to cover evolution equations of second order and of implicit type In addition to the classical heat and wave equations ... Evolution Equations 95 1 Introduction 95 2 The Cauchy Problem 98 v Trang 73 Generation of Semigroups 1006 Analytic Semigroups 113 7 Parabolic Equations 119 V Implicit Evolution Equations

Ngày tải lên: 31/03/2014, 15:56

... p2 = R2=||u||. Then, Equation 7 holds Therefore, by Equations 4 and 7 and the second part of Lemma 2.3, T has a fixed point inP ∩ ( ¯ 2\ 1), which is a positive solution of Equation 1 □ Example ... R2=||u||. Trang 8Then, Equation 12 holds.Therefore, by Equations 10 and 12 and the first part of Lemma 2.3, T has a fixed point inP ∩ ( ¯ 2\ 1), which is a positive solution of Equation 1 □ Example ... concerned with the existence and multiplicity of positive solutions for the following nonlinear differential equation with nonlocal boundary value condi-tion ⎧ ⎪ ⎪ ⎪ ⎪ −  1  0 |u(s)| qdϕ(s)  u(t)

Ngày tải lên: 21/06/2014, 02:20

... pagesdoi:10.1155/2011/483057 Research Article Iterative Solutions of Singular Boundary Value Problems of Third-Order Differential Equation Peiguo Zhang Department of Elementary Education, Heze University, Heze 274000, Shandong, ... obtained are very general and complement previous known results 1 Introduction Third-order differential equations arise in a variety of different areas of applied mathematics and physics, such as the deflection ... for valuable suggestions and comments References 1 M Gregus, “Third order linear Differential equations,” in Mathematics and Its Applications, Reidel, Dordrecht, the Netherlands, 1987 2 L.-J

Ngày tải lên: 21/06/2014, 05:20

... in Difference Equations Volume 2011, Article ID 546038, 14 pages doi:10.1155/2011/546038 Research Article The Existence of Positive Solution to a Nonlinear Fractional Differential Equation with ... fractional differential equations,” Electronic Journal of Differential Equations, no 36, pp 1–12, 2006 16 M Benchohra, S Hamani, and S K Ntouyas, “Boundary value problems for differential equations with ... α−1− h t G1 t, s dt h t tα−1 dt 2.5 Proof By Lemma 1.3, we can reduce the equation of problem 2.1 to an equivalent integral equation x t By x α −I0 y t c1 tα−1 0, there is c2 − c2 tα−2 Γα t α−1 t−s

Ngày tải lên: 21/06/2014, 05:20

... to Lemma 2.6, 1.2 is equivalent to the fractional integral equation 2.7 The integral equation 2.7 is also equivalent to fixed-point equation T u t u t ,u t ∈ C3 0, , where operator T : K → K ... for the fractional diffusion-wave equation,” Applied Mathematics Letters, vol 9, no 6, pp 23–28, 1996 E Buckwar and Y Luchko, “Invariance of a partial differential equation of fractional order under ... differential equations,” Electronic Journal of Differential Equations, vol 36, pp 1–12, 2006 Z B Bai and H S Lu, “Positive solutions for boundary value problem of nonlinear fractional ă dierential equation,

Ngày tải lên: 21/06/2014, 07:20

... 1Volume 2011, Article ID 456426, 19 pagesdoi:10.1155/2011/456426 Research Article Impulsive Differential Equation with Nonlocal Boundary Conditions 1 School of Science, Beijing Information Science ... theory of impulsive differential equations, see Lakshmikantham et al 1; for an overview of existing results and of recent research areas of impulsive differential equations, see Benchohra et al ... of impulsive differential equations has become an important area of investigation in the recent years and is much richer than the corresponding theory of differential equations; see, for instance,3

Ngày tải lên: 21/06/2014, 16:20

... Trang 1This Provisional PDF corresponds to the article as it appeared upon acceptance Fully formattedPDF and full text (HTML) versions will be made available ... will be made available soon Positive solutions for boundary value problem for fractional differential equation with $p$-Laplacian operator Boundary Value Problems 2012, 2012:18 doi:10.1186/1687-2770-2012-18 ... fractional differential equations; fixed point index; p-Laplacian opera-tor; positive solution; multiplicity of solutions 2010 Mathematical Subject Classification: 34A08; 34B18. Differential equations of

Ngày tải lên: 21/06/2014, 17:20

... Trang 1DIFFERENTIAL EQUATIONEDUARDO LIZ AND MIH ´ALY PITUK Received 21 March 2006; Revised 16 August 2006; Accepted ... (1.2), we can associate an initial condition of the formwhereσ ∈ R+andφ ∈ C. Equation (1.2) includes as a special case the equation x (t) = − dx(t − τ) + f x(t − ω) whereτ, ω ∈ R+,d ∈ R, and f ... consider the equation x (t) = ∞  i =1 a i x t − r i +K x t wherea i ∈ Rand 0≤ r i ≤ r for some r > 0 and i =1, 2, ,∞ i =1| a i | < ∞, and K : C → R is a bounded linear functional Equation

Ngày tải lên: 22/06/2014, 21:20

... phenomena. The analysis starts with a second-order differential equation, free of constants, that offers a general way of describ- ing them. This equation is then integrated and applied to illustrative ... showed that the underlying relation describing these phenomena, equation (1), became Δ(dy/dx)/Δ(y/x) = Γ fr , see equation (9). The slope, equation (3), became κ = κ 0 ·(Γ fr ) 2 . Its strong dependence ... curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving

Ngày tải lên: 13/08/2014, 16:20

... stability in delay differential equations, Differential and Integral Equations 3, 181-200, (1990) I Gyiiri, Global attractivity in nonoscillating perturbed linear delay differential equations, In ... delay differential equations, Differential and Integral Equations 3, 181-200, (1990) 9 I Gyiiri, Global attractivity in nonoscillating perturbed linear delay differential equations, ... equation (4.2) is equivalent to the equation t&(t) = -(Ko and by assumption theory its characteristic of delay differential of equation Theorem + E) Faiu,(t i=o equation equations (4.14) is not oscillatory

Ngày tải lên: 29/10/2015, 14:19

... go to www.springer.com/series/223 Haim Brezis Functional Analysis, Sobolev Spaces and Partial Differential Equations 1C Haim Brezis Distinguished Professor Department of Mathematics Rutgers University ... conceived a program mixing elements from two distinct “worlds”: functional analysis (FA) and partial differential equations (PDEs) The first part deals with abstract results in FA and operator theory ... and nonlinear PDEs that arise, for example, in differential geometry, harmonic analysis, engineering, mechanics, and physics They belong to the toolbox of any graduate student in analysis Unfortunately,

Ngày tải lên: 19/05/2017, 07:59

... 1.2.1 Ordinary differential equations 15 1.2.2 Partial differential equations 16 1.3 Exercises 22 2 Equations of first order 25 2.1 Linear equations 25 2.2 Quasilinear equations ... 9Chapter 1Introduction Ordinary and partial differential equations occur in many applications Anordinary differential equation is a special case of a partial differential equa-tion but the behaviour ... problems is the theory ofordinary differential equations This is quite different for systems of partialdifferential of first order The general linear partial differential equation of first order can

Ngày tải lên: 11/06/2017, 20:16

... tia l equations in Hilbert, spaces Besides, we d iscu ss the relatio n between p ro p ­ erties o f solutions o f differential equations of tria n g u la r fo r m and those, o f truncated differential ... la r fo r m and those, o f truncated differential equations I Introduction Let us consider in a given separable Hilbert space // differential equations of the form ( 1 ) ( ) where / : I V X H ... o ) ĩ Xo € H o f equation (1) the following relation t-Qì Pm%o) tư) Pm ^o) holds fo r all t : /? 4, 771 ỗ J , Xo G // Pvoof For given rn e J , lot us consider the differential equation -T” = /(*,

Ngày tải lên: 14/12/2017, 19:52

... hyperbolic partial differential equations Hoang Viet Long · Nguyen Thi Kim Son · Nguyen Thi My Ha · Le Hoang Son © Springer Science+Business Media New York 2014 Abstract Fuzzy hyperbolic partial differential ... develop-ment of calculus for fuzzy functions, the investigation of fuzzy differential equations(DEs) and fuzzy partial differential equations (PDEs) have been initiated (Buckleyand Feuring 1999;Seikkala ... illustrativeexamples with some numerical simulations forα-cuts of fuzzy solutions. Keywords Fuzzy partial differential equation· Fuzzy solution · Integral boundarycondition· Local initial condition · Fixed

Ngày tải lên: 16/12/2017, 08:45