solving system of nonlinear partial differential equations
báo cáo hóa học: " Exponential energy decay and blow-up of solutions for a system of nonlinear viscoelastic wave equations with strong damping" ppt
... decay of solutions for a quaslinear system of viscoelastic equations Nonlinear Anal 71, 2257–2267 (2009) doi:10.1016/j.na.2009.01.060 22 Agre, K, Rammaha, MA: Systems of nonlinear wave equations ... (2006) 23 Said-Houari, B, Messaoudi, SA, Guesmia, A: General decay of solutions of a nonlinear system of viscoelastic wave equations Nonlinear Diff Equ Appl (2011) 24 Muñoz Rivera, JE: Global solution ... 19 Han, XS, Wang, WM: Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source Nonlinear Anal 71, 5427–5450 (2009) doi:10.1016/j.na.2009.04.031...
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báo cáo hóa học:" Research Article Minimal Nonnegative Solution of Nonlinear Impulsive Differential Equations on Infinite Interval" pot
... investigate the existence of minimal nonnegative solution for a class of second-order nonlinear impulsive differential equations on an infinite interval with an infinite number of impulsive times Consider ... Jurisdiction of Beijing Municipality PHR201008430 , the Scientific Research Common Program of Beijing Municipal Commission of Education KM201010772018 , the 2010 level of scientific research of improving ... impulsive differential equations, ” Nonlinear Analysis: Theory, Methods & Applications, vol 25, no 4, pp 327–337, 1995 D Guo, “Existence of solutions of boundary value problems for nonlinear second...
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Báo cáo hóa học: "ON DISCRETE ANALOGUES OF NONLINEAR IMPLICIT DIFFERENTIAL EQUATIONS" docx
... analogues of nonlinear implicit differential equations convergence of the explicit Euler method for nonlinear index-1 DAEs is established The results of this section are a nonlinear version” of the ... applied to nonlinear DAEs and PDAEs lead to nonlinear IDEs In this paper the unique solvability of discretized problems obtained via discretization of nonlinear implicit differential equations ... also an index-1 IDE Proof For the proof of the theorem we first reduce (2.6) to its normal form (2.3) Then we will show that (2.3) is of index-1 by verifying all the conditions of Definition 2.1 Let...
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Báo cáo hóa học: " Positive solutions for a coupled system of nonlinear differential equations of mixed fractional orders" pot
... system of nonlinear fractional differential equations Int J Differ Equ 2010, 2010:1-12 28 Ahmad B, Nieto JJ: Existence results for a coupled system of nonlinear fractional differential equations ... uniqueness of solutions for coupled systems of higher-order nonlinear fractional differential equations Fixed Point Theory Appl 2010, 2010:1-17 30 Babakhani A: Positive solutions for system of nonlinear ... problems of N-Dimension nonlinear fractional differential system Bound Value Probl 2008, 2008:1-15 24 Bai C, Fang J: The existence of a positive solution for a singular coupled system of nonlinear...
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Tài liệu Báo cáo " Fully parallel methods for a class of linear partial differential-algebraic equations " pptx
... Splitting-up Method for Partial Differential Equations and Its Apptications to Navier-Stockes Equations, Applied Mathematics Letters Vol 4, No (1992) 25 Vu Tien Dung / VNU Journal of Science, Mathematics ... Discretizing the BVP (12)-(13) one obtains a large-scale system of linear equations Lw = g, (19) where L is a symmetric positive define matrix of dimension p × p, where p = p(h) depends on the discretization ... number of iterations needed for convergence and the total time for the serial computation of Red - Black SOR and Jacobi method are given in the following tables Table Number of Iterations of sequential...
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Báo cáo hóa học: " Solving systems of nonlinear matrix equations involving Lipshitzian mappings" pdf
... classes of nonlinear matrix equations (see [8-21]) In this study, we consider the following problem: Find (X1, X2, , Xm) Î (P(n))m solution to the following system of nonlinear matrix equations: ... Duan, F: Positive defined solution of two kinds of nonlinear matrix equations Surv Math Appl 4, 179–190 (2009) Hasanov, V: Positive definite solutions of the matrix equations X ± A*X-q A = Q Linear ... 2011:89 http://www.fixedpointtheoryandapplications.com/content/2011/1/89 Page of 10 3.2 System of three nonlinear matrix equations We consider the problem: Find (X1, X2, X3) Î (P(n))3 solution to...
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báo cáo hóa học: " Some new results for BVPs of first-order nonlinear integro-differential equations of volterra type" doc
... conditions x(0) = -x(1) The authors of [20-24] consider this kind of “anti-periodic” conditions for differential equations or impulsive differential equations To the best of our knowledge it is the first ... integro -differential equation of Volterra type on time scales Nonlinear Anal 60, 429–442 (2005) Xing, Y, Ding, W, Han, M: Periodic boundary value problems of integro -differential equations of Volterra ... Advances in Difference Equations 2011, 2011:14 http://www.advancesindifferenceequations.com/content/2011/1/14 Page of 17 It completes the proof Now consider the existence of solutions of PBVP (1.1) It...
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Báo cáo hóa học: " Research Article Necessary Conditions of Optimality for Second-Order Nonlinear Impulsive Differential Equations" docx
... Existence of optimal controls In this section, we not only present the existence of PCl -mild solution of the controlled system (1.1) but also give the existence of optimal controls of systems ... 2 Advances in Difference Equations technique to derive the maximum principle for a Lagrange problem of systems governed by a class of the second-order nonlinear impulsive differential equation ... estimate of mild solution in space C (I,X) which can be proved by Gronwall lemma Step by step, the existence of PCl -mild solution of (3.1) can be derived Let xu denote the PCl -mild solution of system...
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Báo cáo hóa học: " Research Article Existence of Solutions for Second-Order Nonlinear Impulsive Differential Equations with Periodic Boundary Value Conditions" potx
... superlinear growth of the nonlinearity of f (t, p) in p Inspired by [21, 24, 25], in this paper, we investigate the following second-order impulsive nonlinear differential equations with periodic ... ordinary differential equations, ” Nonlinear Analysis, vol 51, no 7, pp 1223–1232, 2002 [24] C Bai, “Existence of solutions for second order nonlinear functional differential equations with periodic ... no 1, pp 51–59, 2000 [17] L Chen and J Sun, Nonlinear boundary value problem of first order impulsive functional differential equations, ” Journal of Mathematical Analysis and Applications, vol...
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Báo cáo hóa học: "ENTIRE POSITIVE SOLUTION TO THE SYSTEM OF NONLINEAR ELLIPTIC EQUATIONS" docx
... ∈ RN The proof of Lemma 3.1 is given for completeness in the appendix of this article Lemma 3.2 is an extension of [17, Lemma 1], so the proof is omitted here for briefness Proof of Theorem 2.1 ... existence of positive entire solutions cannot be derived from those in the literature The aim of this article is to develop the theory of existence of positive solutions for nonlinear elliptic systems ... positive equilibrium solutions to system (1.5) in RN are corresponding to the entire positive solutions of a system in the form of (1.1) Some existence results of elliptic system Δu + F1 (x,u,v) = 0,...
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Báo cáo y học: "Modelling of oedemous limbs and venous ulcers using partial differential equations" pdf
... sorts of measurement methods is not often portable and is often costly, thus making it prohibitive for routine medical use The aim of this paper is to show how it is possible to develop a system ... measurement of the amount of oedema as well as the area and volume of the ulcer wounds This is because without an accurate and objective means of measuring changes in the size or shape of ulcers, ... exponential functions The specific forms of A0 (u), An (u), Bn (u) and R(u, v) for the case of Equations (1) can be found in [17] and for the case of Equations (2) can be found in [21] The main...
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Partial Differential Equations part 1
... What are the variables? • What equations are satisfied in the interior of the region of interest? • What equations are satisfied by points on the boundary of the region of interest? (Here Dirichlet ... the solution of large numbers of simultaneous algebraic equations When such equations are nonlinear, they are usually solved by linearization and iteration; so without much loss of generality ... − 4uj,l = ∆2 ρj,l (19.0.6) To write this system of linear equations in matrix form we need to make a vector out of u Let us number the two dimensions of grid points in a single one-dimensional...
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Partial Differential Equations part 2
... third type of error is one associated with nonlinear hyperbolic equations and is therefore sometimes called nonlinear instability For example, a piece of the Euler or Navier-Stokes equations for ... j 838 Chapter 19 Partial Differential Equations stable unstable ∆t ∆t ∆x ∆x x or j (a) ( b) Figure 19.1.3 Courant condition for stability of a differencing scheme The solution of a hyperbolic ... rewritten as 840 Chapter 19 Partial Differential Equations Other Varieties of Error ξ = e−ik∆x + i − v∆t ∆x sin k∆x (19.1.25) An arbitrary initial wave packet is a superposition of modes with different...
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Tài liệu Partial Differential Equations part 3 pptx
... 19 Partial Differential Equations The physical interpretation of the restriction (19.2.6) is that the maximum allowed timestep is, up to a numerical factor, the diffusion time across a cell of ... Dividing by α, we see that the difference equations are just the finite-difference form of the equilibrium equation 850 Chapter 19 Partial Differential Equations t or n (a) x or j Fully Implicit ... (19.2.22) with n → n + leaves us with a nasty set of coupled nonlinear equations to solve at each timestep Often there is an easier way: If the form of D(u) allows us to integrate dz = D(u)du (19.2.23)...
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Tài liệu Partial Differential Equations part 4 ppt
... boundary value problems (elliptic equations, for example) reduce to solving large sparse linear systems of the form A·u=b (19.4.1) either once, for boundary value equations that are linear, or iteratively, ... (19.3.16) The advantage of this method is that each substep requires only the solution of a simple tridiagonal system Operator Splitting Methods Generally The basic idea of operator splitting, ... These will occupy us for the remainder of the chapter CITED REFERENCES AND FURTHER READING: Ames, W.F 1977, Numerical Methods for Partial Differential Equations, 2nd ed (New York: Academic Press)...
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Tài liệu Partial Differential Equations part 5 ppt
... level of CR, we have reduced the number of equations by a factor of two Since the resulting equations are of the same form as the original equation, we can repeat the process Taking the number of ... North America) ∂u = g(y) ∂x 862 Chapter 19 Partial Differential Equations The finite-difference form of equation (19.4.28) can be written as a set of vector equations uj−1 + T · uj + uj+1 = gj ∆2 ... Helmholtz or Poisson equations in polar, cylindrical, or spherical coordinate systems More general separable equations are treated in [1] Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...
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Tài liệu Partial Differential Equations part 6 doc
... for solving a larger problem once only, where ease of programming outweighs expense of computer time Occasionally, the sparse matrix methods of §2.7 are useful for solving a set of difference equations ... Chapter 19 Partial Differential Equations ADI (Alternating-Direction Implicit) Method The ADI method of §19.3 for diffusion equations can be turned into a relaxation method for elliptic equations ... application of the above results, consider our model problem for which ρJacobi is given by equation (19.5.11) Then equations (19.5.19) and (19.5.20) give 868 Chapter 19 Partial Differential Equations...
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Tài liệu Partial Differential Equations part 7 doc
... 872 Chapter 19 Partial Differential Equations From One-Grid, through Two-Grid, to Multigrid The key idea of the multigrid method can be understood by considering the simplest case of a two-grid ... current value of the solution u[1 n][1 n], using the right-hand side function rhs[1 n][1 n] { int i,ipass,isw,j,jsw=1; double h,h2; 882 Chapter 19 Partial Differential Equations Nonlinear Multigrid: ... algorithm we will have to consider equations where a nonzero right-hand side is generated during the course of the solution: Lh (uh ) = fh (19.6.23) One way of solving nonlinear problems with multigrid...
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Functional analysis sobolev spaces and partial differential equations
... proof of the Krein–Milman theorem, see Problem (b) In the theory of partial differential equations Let us mention, for example, that the existence of a fundamental solution for a general differential ... analysis (FA) and partial differential equations (PDEs) The first part deals with abstract results in FA and operator theory The second part concerns the study of spaces of functions (of one or more ... {x ∈ E ; p(x) < 1} ∀x ∈ E, Proof of Lemma 1.2 It is obvious that (1) holds Proof of (9) Let r > be such that B(0, r) ⊂ C; we clearly have p(x) ≤ x r ∀x ∈ E Proof of (10) First, suppose that x...
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Tài liệu AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS ppt
... while u + u = is a nonlinear equation The nonlinear equations are often further x y classified into subclasses according to the type of the nonlinearity Generally speaking, the nonlinearity is more ... a nonlinearity is called quasilinear On the other hand in (1.2) the nonlinearity is only in the unknown function Such equations are often called semilinear r Scalar equations versus systems of ... systems of equations A single PDE with just one unknown function is called a scalar equation In contrast, a set of m equations with l unknown functions is called a system of m equations 1.3 Differential...
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