solutions of the diffusion equation
Báo cáo hoa học: " Research Article On Boundedness of Solutions of the Difference Equation xn 1 pxn qxn−1 / 1 xn for q 1 p 1" pot
... 1.Let S be the set of all initial values x−1,x0 ∈ 0, ∞ × 0, ∞ such that the positive solutions {xn}∞n−1 of 1.1 are bounded. Then we have the following theorem.Theorem 3.6. ... 2.7. The proof of Lemma 2.3 is completed.3. Main ResultsIn this section, we investigate the boundedness of solutions of 1.1.Letq>1 p>1, andlet {xn}∞n−1be a positive solution of ... Eventually, one of them is monotonically increasing, and the other is monotonicallydecreasing.Remark 3.3. Using arguments similar to ones in the proof of Lemma 3.2,Stevi´c provedTheorem 2 in...
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Numerical Solutions of the Black Scholes Equation
... we have got the stability conditions right, we can forget about convergence.908 Numerical Solutions of the Black Scholes Equation The left-hand side of the heat equation, on the other hand, ... solution of the Kolmogorov backward equation; there-fore the binomial model is a graphical representation of the Kolmogorov equation. r The explicit difference method was introduced to solve the ... designated by the vector s0. The second column in the grid can therefore be obtained by using the equation Ap1= s0. And so the process can be repeated across the grid, merely by solving the equations...
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Tài liệu Đề tài " Rough solutions of the Einstein-vacuum equations " docx
... but also the fact that they are themselves solutions to asimilar system of equations. This allowed us to improve the exponent s, neededin the proof of well-posedness of equations of type (6),8to ... proof of the Main Theorem with the exception of those results whichconcern the asymptotic properties of the Ricci coefficients (the AsymptoticsTheorem), and the straightforward modifications of the ... right-handside of (14) vanishes identically. We make use of both the vanishing of the Ricci curvature of g and the wave coordinate condition (2). The other impor-tant new features are the use of energy...
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Báo cáo hóa học: " On the behavior of solutions of the system of rational difference equations" pptx
... EM: On the solutions of a class of difference equations systems. DemonstratioMathematica. 41(1), :109–122 (2008)32. Elsayed, EM: On the solutions of a rational system of difference equations. ... positive solutions of the system of rational difference equa-tionsxn+1=1yn−k, yn+1=ynxn−myn−m−k.In [9], Zhang et al. investigated the behavior of the positive solutions of the system of ... behavior of a three-dimensional linear fractional system of difference equations. JMath Anal Appl. 310, 673–689 (2005)8. Özban, AY: On the positive solutions of the system of rational difference equationsxn+1=1yn−k,yn+1=ynxn−myn−m−k.....
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Báo cáo hóa học: "Global behavior of the solutions of some difference equations" pptx
... and rewarding, and the results about these equations offer prototypestowards the de velopment of the basic theory of the global behavior of nonlinear differ-ence equation s of a big order, recently, ... investigated the behavior of the solutions, HAE-M found the solutions of the special cases and EMEls carriedout the theoretical proof and gave the examples. All authors read and approved the final ... every solution of Equation 2 converges to¯xProof: As the proof of Theorem 2 and will be omitted.Theorem 4 The equilibrium point¯x of Equation 1 is global attractor if c ≠ a.Proof: Let p, q...
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Báo cáo hóa học: " Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument" ppt
... mentioning that the condit ions of our theorems are easily toverify, so they are applicable to a variety of problems, see Examples 4.1 and 4.2. The proof of our main resul ts is based upon the following ... equations.Toidentifyafew,wereferthereaderto[2-13] and the references therein.Fractional differential equations arise in many engineering and scientific disciplinesas the mathematical modeling of systems and processes in the fields of ph ... η)1 −βη, η}.Proof.Notethatu“ (t) ≤ 0, by applying the concavity of u,theproofiseasy.Soweomit it.3 Proofs of main theoremsDefine the operator T : C[0, 1] ® C[0, 1] as follows,Tu(t)=−t0(t...
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báo cáo hóa học:" Research Article Existence and Nonexistence of Global Solutions of the Quasilinear Parabolic Equations with Inhomogeneous Terms" pot
... extension of the results of 8.Ifweputσ 0inthese theorems, the same results as Theorem 1 in 8 are obtained.We will prove Theorem 1.1a and b in Sections 3 and 4, respectively. The proof of Theorem ... parabolic equations on manifolds,” Duke MathematicalJournal, vol. 97, no. 3, pp. 515–539, 1999.10 Y W. Qi, The critical exponents of parabolic equations and blow-up in Rn,” Proceedings of the ... ≤−1. This p∗m,σis called the critical exponent.On the other hand, 6–9 and so on. study the inhomogeneous equations i.e., fx/≡ 0in 1.1.Bandleetal.6 study the case m 1, σ 0, and...
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báo cáo hóa học:" Research Article A Remark on the Blowup of Solutions to the Laplace Equations with Nonlinear Dynamical Boundary Conditions" pdf
... years, the problem has attracted a great deal of people. Lions6 used the theory of maximal monotone operators to solve the existence of solution of the following problem:Δu 0, in Ω ×0,T, ... Journal of Qualitative Theory of Differential Equations, no. 13, pp. 1–20, 2008.30 E. Vitillaro, “On the Laplace equation with non-linear dynamical boundary conditions,” Proceedings of the London ... ArticleA Remark on the Blowup of Solutions to the Laplace Equations with Nonlinear DynamicalBoundary ConditionsHongwei Zhang and Qingying HuDepartment of Mathematics, Henan University of Technology,...
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Báo cáo hóa học: " Research Article Existence of Pseudo Almost Automorphic Solutions for the Heat Equation with Sp -Pseudo Almost Automorphic Coefficients" docx
... α∞n1nn−1s−qαe−qγsds1/q< ∞,thenΓ3u ∈ PAAXα.Proof. The proof is similar to that of Lemma 5.3 and hence omitted, though here we make use of the approximation 5.4 rather than 5.5.Throughout the rest of the ... the techniques of hyperbolic semigroups to study the existence of pseudo almost automorphic solutions to the class of partial hyperbolic differentialequations appearing in 1.3 and then to the ... automorphic solutions to the partial hyperbolic differential equations of the form 1.3 have recently been establishedin 12, 15–18, respectively. Though to the best of our knowledge, the existence of...
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Báo cáo hóa học: " Research Article Global Existence and Uniqueness of Strong Solutions for the Magnetohydrodynamic Equations" potx
... this is crucial in the proof of the uniqueness of strong solutions. 3. Global existence of strong solutions In this section, we prove the global existence of strong solutions to the problem 1.2–1.7 ... completes the proof of Theorem 1.1 except the uniqueness assertion because of the presence of vacuum, which will be proved in the nextsection.4. Uniqueness and stability of strong solutions In ... and H. Kim, “Global existence of the radially symmetric solutions of the Navier-Stokesequations for the isentropic compressible fluids,” Mathematical Methods in the Applied Sciences, vol. 28,no....
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Báo cáo hóa học: "Research Article The C1 Solutions of the Series-Like Iterative Equation with Variable Coefficients/; potx
... solution f ∈AN1,N2.Proof. The existence of 1.2 in AN1,N2 is given by Theorem 3.1, from the proof of Theorem 3.1,weseethatAN1,N2 is a closed subset of C1I,I,by3.12 and ... “Stability of the solution of the iterated equation ni1λifixFx,” Acta MathematicaScientia, vol. 8, no. 4, pp. 421–424, 1988.4 W. N. Zhang, “Discussion on the differentiable solutions of ... functional equations in the class of Lipschitz functions,”Aequationes Mathematicae, vol. 64, no. 1-2, pp. 24–33, 2002.7 X. P. Li, “A class of iterative equation on a Banach space,” Journal of Sichuan...
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Báo cáo hóa học: " On the stability of the exact solutions of the dual-phase lagging model of heat conduction" docx
... carried out the mathematical calculations, participated in the interpretations of the results and drafted the manuscript. JJAG conceived of the study, participated in the analysis of the results ... prece-dence of the heat flux vector to the temperature gradi-ent at all. In fact, whether the heat flux vect or precedes the temperature gradient or not depends on the com-bined effects of the thermal ... a[m2.s-1] is the thermal diffusivity of the med-ium, and t = tq-tTis the difference of the phase lags. Equation 2 shows explicitly that the DPL and SPL mod-els, both in their exact form,...
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báo cáo hóa học:" Research Article A Discrete Equivalent of the Logistic Equation" potx
... explicitly solved using the z-transform method. The connection of the solution of the discrete equivalent logistic equation with the solution of the logistic differential equation is discussed. ... meansunlike the known versions of discrete logistic equation such as 1.4. Thus, the solutions of 1.8 are expected to have similar behavior with those of the differential logistic equation and not the ... differences of the discrete equivalent logistic equation and the well-known discrete analogue of the logistic equation are mentioned. It is hopedthat this discrete equivalent of the logistic equation...
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báo cáo hóa học:" Research Article Almost Periodic Viscosity Solutions of Nonlinear Parabolic Equations" potx
... viscosity solutions. We consider the following two equations to get some results used for the existence anduniqueness of almost periodic viscosity solutions. That is, the Dirichlet problems of the ... studied the time periodic and almost periodic viscosity solutions of first-order Hamilton-Jacobi equations. Nunziante considered the existence and uniqueness of viscosity solutions of parabolic equations ... .3.21Now we have the following.2 Boundary Value Problems the proof of existence of viscosity solutions of first-order Hamilton-Jacobi equations, Crandallet al. had applications of Perron’s Method...
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Báo cáo hóa học: " Research Article The Periodic Character of the Difference Equation xn 1 f xn−l 1, xn−2k 1" pdf
... M.2.23 The proof is complete.Remark 2.2. 1 The proofs of Lemma 2.1 and Theorem 1.1 draw on ideas from the proofs of Theorems 2.1 and 2.2 in 6.2 Consider the nonlinear difference equation xn1 ... difference equation and deal with the question of whether every positive solution of this equation converges to a periodic solution. Recently,there has been a lot of interest in studying the global ... limx→∞gxa. The main result of this paper is the following theorem.Theorem 1.1. Every positive solution of 1.1 converges to (not necessarily prime) a 2-periodic solu-tion.2. Proof of Theorem...
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- the standard form of the equation
- the problem of the equation
- the application of partial differential equation
- write the standard form of the equation y 4 127x1
- write the standard form of the equation calculator
- identify the standard form of the equation 13x 73y 2
- determine the standard form of the equation
- finding the standard form of the equation for a conic section
- write the standard form of the equation
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