transient equations with longitudinal conduction and wall thermal storage

Ngày tải lên: 12/06/2014, 16:17

... phosphate buffer at pH 5.8 and 8.0 Materials and methods Results and discussion Protein production and purification The purification of wild-type Cel7A enzyme and the E217Q and E223S/A224H/L225V/T226A/D262G ... values (Fig 3B and D), indicative of the release of the substrate Comparison of the Cel7A unfolding with and without the substrate either at pH 8.0 (Fig 3A and B), or pH (Fig 3C and D) shows interestingly ... wild-type Cel7A and pH mutant E223S/A224H/L225V/T226A/D262G at pH 5.8 and pH 8.0 and 25 °C Spectra of the wild-type Cel7A at pH 5.8 (d) and pH 8.0 (s), and the pH mutant at pH 5.8 (j) and pH 8.0 (h)...

Ngày tải lên: 31/03/2014, 07:20

... Functional differential equations with state-dependent delays: theory and applications Handbook of Differential Equations: Ordinary Differential Equations, vol III Elsevier/North-Holland, Amsterdam (2006), ... Remark 2, the lower solution α and the upper solution β satisfy, respectively, inequalities (7) and (8) and, conversely, if α and β satisfy (7) and (8) then they are lower and upper solutions in the ... as in (18) with m = ϕ∗ −y L satisfies that β(t) ≥ k(t) for all t ∈ I− and β (t) = m ≥ max y≤maxI β(t) f (y) for all t ∈ I0 (25) So we deduce from (24) and (25) that α and β are lower and upper...

Ngày tải lên: 20/06/2014, 20:20

... Existence and multiplicity of solutions for nonlocal p(x)-Laplacian equations with nonlinear Neumann boundary conditions Erlin Guo∗ and Peihao Zhao School of Mathematics and Statistics, ... equation with the nonlinearity f satisfying Ambrosetti–Rabinowitz condition The p(x)-Kirchhoff type equations with Dirichlet boundary value problems have been studied by Dai and Hao [24], and much ... problems with variable exponent are interesting in applications and raise many difficult mathematical problems We refer the readers to [17–23] for the study of p(x)-Laplacian equations and the corresponding...

Ngày tải lên: 20/06/2014, 21:20

... > 0, and proved a global existence result for g ≥ and an exponential decay for g > This result has been extended by Messaoudi and Tatar [2,7] to the situation where g = and exponential and polynomial ... accommodate certain solutions with positive initial energy Song and Zhong [13] considered (1.2) for h(ut) = -Δut and f(u) = |u|p-2u and proved a blow-up result for solutions with positive initial energy ... Said-Houari and Messaoudi [23] and Messaoudi and Said-Houari [20] So throughout this article, we have assumed that n ≤ (G2) max ∞ ∞ g1 (s)ds, g2 (s)ds < Theorem 2.1 Assume that (2.1) and (G1) hold, and...

Ngày tải lên: 21/06/2014, 00:20

... measure the thermal conductivity The inner diameter and length of long glass container are 19 and 240 mm, respectively The transient hot wire system was calibrated with D.I water and ethylene ... vol.%) and the thermal conductivity was increased up to 1.3% at room temperature without surfactant and surface treatment The addition of dispersant and surfactant would make the MWNT coated and ... were conducted with and without the addition of MWNT/water nanofluid The test system included a base fluid loop and a water loop The base fluid could be supplied with either water or with nanofluid;...

Ngày tải lên: 21/06/2014, 04:20

... either to scalar equations without time delays or to coupled system of equations without time delays and with the restrictive conditions that the principal parts are the same and the convection ... the method of upper and lower solutions and the monotone iteration scheme to reaction-diffusion system with discontinuous coefficients and continuous delays and use these methods and the results of ... show that u1 and u1 are well defined and possess the properties 2.30 and 2.31 for m Assume, by induction, that um and um given by 2.29 are well defined and possess l the properties 2.30 and 2.31 ...

Ngày tải lên: 21/06/2014, 05:20

... , and Yμ and operators Ai t , Biν , Ckν t , j and Dkμ , and traces theorems see 3, chapter , where k 1, 2, , m; ν i 1, 2, , m; μ 1, 2, , rj ; j 1, 2, , m The linear manifolds H0 and ... Yakubov and Y Yakubov, Differential-Operator Equations Ordinary and Partial Differential Equations, vol 103 of Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, Chapman & Hall/CRC, ... that linear operators Ai t , Biν , Ciν t , and Diμ and the nonlinear operators Fi , Gi1 , and Gi2 , i 1, , m satisfy the conditions of Theorem 2.1, and the problem 3.1 is represented as an abstract...

Ngày tải lên: 21/06/2014, 11:20

... Difference Equations For quasi-linear parabolic equations, the authors of 1–5 and so on study the homogeneous equations i.e., f x ≡ in 1.1 Baras and Kersner proved that 1.1 with m and f x ≡ has ... σ > −2 and for N 1, σ > −1, pm,σ m for N 1, ∗ σ ≤ −1 This pm,σ is called the critical exponent On the other hand, 6–9 and so on study the inhomogeneous equations i.e., f x / ≡ in 1.1 Bandle et ... Journal of Differential Equations, vol 68, no 2, pp 238–252, 1987 K Mochizuki and K Mukai, “Existence and nonexistence of global solutions to fast diffusions with source,” Methods and Applications of...

Ngày tải lên: 21/06/2014, 11:20

... “Fixed points and stability in differential equations with variable delays,” Nonlinear Analysis: Theory, Methods and Applications, vol 63, no 5–7, pp e233–e242, 2005 L C Becker and T A Burton, ... stable if and only if 1.3 is iii t a h s ds −→ ∞, as t −→ ∞ 1.9 Fixed Point Theory and Applications Theorem 1.3 Burton Suppose that r t r, a constant Let f be odd, increasing on 0, L , and satisfies ... L1 , s−r and there exists J > such that t − r ds ≤ J a s for t ≥ 1.11 Then, the zero solution of 1.4 is stable Theorem 1.4 Becker and Burton Suppose f is odd, strictly increasing, and satisfies...

Ngày tải lên: 21/06/2014, 11:20

... 19 , Karakostas and Tsamatos 20 , Lomtatidze and Malaguti 21 , and the references therein For more information about the general theory of integral equations and their relation with boundaryvalue ... , 0, ∞ and may be singular at t or t 1; f, g : 0, × P \ {θ} × 0; , bi , ci , and P \ {θ} → P are continuous and may be singular at t 0, 1, u 0, and u di ∈ 0, ∞ , and ρi ci di bi ci > 0, and mi ... points with t0 < t1 < t2 < · · · < tk < · · · < tm < tm 1, Δx |t tk x tk − x t− , where x tk and x t− represent the right-hand limit and left-hand k k limit of x t at t tk , respectively, and g,...

Ngày tải lên: 21/06/2014, 16:20

... equation with a deviating argument,” Journal e of Computational and Applied Mathematics, vol 214, no 1, pp 13–18, 2008 W.-S Cheung and J Ren, “Periodic solutions for p-Laplacian Li´ nard equation with ... following assumptions hold: A1 g ∈ C1 R, R and g x < for all x ∈ R; A2 there exist a constant r ≥ and a function ε t ∈ C R, R such that for all t ∈ R and |x| > r, x g x −ε t T < 0, T ε t − e t ... solution with period T to 1.1 Advances in Difference Equations Uniqueness Let x ψ x f u du, y t ϕ x t 2.30 ψ x t Then 1.1 is transformed into x t ϕ−1 y t − ψ x t y t −g x t , 2.31 e t Let x1 t and...

Ngày tải lên: 21/06/2014, 18:20

... study Volterra integro differential equations and retarded differential equations see 14 Definition 2.5 Let X be a Banach space, and let A be a linear operator with domain D A One says that A, ... notations C R; Z and BC R; Z stand for the collection of all continuous functions from R into Z and the Banach space of all bounded continuous functions from R into Z endowed with the uniform ... References D Bugajewski and G M N’Gu´ r´ kata, “On the topological structure of almost automorphic ee and asymptotically almost automorphic solutions of differential and integral equations in abstract...

Ngày tải lên: 21/06/2014, 20:20

... Mathematics and Its Applications, Hindawi, Cairo, Egypt, 2007 N V Azbelev and P M Simonov, Stability of Differential Equations with Aftereffect, vol 20 of Stability and Control: Theory, Methods and Applications, ... Difference Equations, vol 2009, Article ID 671625, 15 pages, 2009 N V Azbelev, V P Maksimov, and L F Rakhmatullina, Introduction to the Theory of Functional Differential Equations: Methods and Applications, ... Van Nostrand, Princeton, NJ, USA, 1962 L Berezansky and E Braverman, “Nonoscillation of a second order linear delay differential equation with a middle term,” Functional Differential Equations, ...

Ngày tải lên: 21/06/2014, 20:20

... points and stability in differential equations with variable delays,” Nonlinear Analysis, vol 63, no 5–7, pp e233–e242, 2005 V B Kolmanovskii and L E Shaikhet, “Matrix Riccati equations and stability ... pp 3679–3687, 2004 T A Burton and T Furumochi, “Fixed points and problems in stability theory for ordinary and functional differential equations, ” Dynamic Systems and Applications, vol 10, no 1, ... c t , e t , q t ∈ C R , R , and τ t , δ t ∈ C R , R with t − τ t → ∞ and t − δ t → ∞ as t → ∞ Here C S1 , S2 denotes the set of all continuous functions φ : S1 → S2 with the supremum norm · In...

Ngày tải lên: 21/06/2014, 23:20

... elliptic equations with p, q-growth conditions,” Journal of Differential Equations, vol 90, no 1, pp 1–30, 1991 [10] Q Zhang, “A strong maximum principle for differential equations with nonstandard ... Journal of Inequalities and Applications Here and hereafter, we will use the notation d(x,∂Ω) to denote the distance of x ∈ Ω to the boundary of Ω Denote d(x) = d(x,∂Ω) and ∂Ω = {x ∈ Ω | d(x) ... is easy to see that (P) possesses only one positive solution, and uλ is increasing with respect to λ 6 Journal of Inequalities and Applications Asymptotic behavior of positive solutions In the...

Ngày tải lên: 22/06/2014, 18:20

... ≡ and f verifies (H3 ), Ruiz has proved that the problem (P)0 has a bounded positive solution (see [2] and reference therein) On the other hand, when f (x,u,η) = u p and g(x,u,η) = uq , q > p and ... Equations, vol 199, no 1, pp 96–114, 2004 [3] C Azizieh and P Cl´ ment, “A priori estimates and continuation methods for positive solutions e of p-Laplace equations, ” Journal of Differential Equations, ... Heriberto Roman and Yurilev a L Iturriaga and S Lorca 11 Chalco for their comments and the fruitful discussions The first author was partially supported by FONDECYT no 3060061 and FONDAP Matem´...

Ngày tải lên: 22/06/2014, 19:20

... difference equations, ” Journal of Difference o Equations and Applications, vol 1, no 2, pp 99–116, 1995 [8] S Elaydi, S Murakami, and E Kamiyama, “Asymptotic equivalence for difference equations with ... Agarwal, Difference Equations and Inequalities, vol 228 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2nd edition, 2000 [3] C T H Baker and Y Song, “Periodic ... edition, 1999 [6] S Elaydi and S Zhang, “Stability and periodicity of difference equations with finite delay,” Funkcialaj Ekvacioj, vol 37, no 3, pp 401–413, 1994 [7] S Elaydi and I Gy¨ ri, “Asymptotic...

Ngày tải lên: 22/06/2014, 22:20

... Kordonis and Philos [7] and Kordonis et al [8], respectively The results in [7, 8] concern difference equations with discrete variable For some related results for difference equations (with discrete ... linear difference equations with continuous time, Differential Equations Dynam Systems (1993), no 4, 311–324 R D Driver, Some harmless delays, Delay and Functional Differential Equations and Their Applications ... 2 Difference equations with continuous variable Philos [11], Kordonis et al [6], and Philos and Purnaras [12] For some related results, we refer to Graef and Qian [5] Moreover, the...

Ngày tải lên: 23/06/2014, 00:20

... differential equations with impulses, Nonlinear Anal 32 (1998), no 6, 775–786 A Cabada, E Liz, and S Lois, Green’s function and maximum principle for higher order ordinary differential equations with ... first order with periodic boundary conditions, Differential Equations Dynam Systems (1993), no 3, 185–196 J Qi and K Wang, Upper and lower solutions for impulsive differential equations with application ... R is a continuous function and it is nonincreasing with respect to its first variable (I) I is continuous and strictly increasing with respect to the first variable and nonincreasing in the second...

Ngày tải lên: 23/06/2014, 00:20