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Optimal control problems for differential equations applied to tumor growth: state of the art

0.01 q 1 Penalty/weight in the objective for the average number of cancer cells in G 1 /G 0 during therapy 1, resp. 0.1 q 2 Penalty/weight in the objective for the average number of cancer cells in S during therapy 1, resp. 0.1 q 3 Penalty/weight in the objective for the average number of cancer cells in G 2 /M during therapy 1, resp. 0.1 r 1 Penalty/weight in the objective for the average number of cancer cells in G 1 /G 0 at the end of therapy 1, resp. 8.25 r 2 Penalty/weight in the objective for the

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Influence of velocity slip and temperature jump conditions on the peristaltic flow of a Jeffrey fluid in contact with a Newtonian fluid

slip condition, J. Appl. Fluid Mech . 8(3) (2015) 521- 528. 10.18869/acadpub.jafm.67.222.23047 Ravikumur G. Radhakrishnamacharya G. Effect of homogeneous and heterogeneous chemical reactions on peristaltic transport of a Jeffrey fluid through a porous medium with slip condition J. Appl. Fluid Mech 8 3 2015 521 528 [25] P. G. Saffman, On the Boundary Conditions at the Surface of a Porous Medium, Stud. Appl. Math . 1 (1971) 93-101. Saffman P. G. On the Boundary Conditions at the Surface of a Porous Medium Stud. Appl. Math 1 1971 93 101 [26] A.H. Shapiro, M

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Non-autonomous perturbations of a non-classical non-autonomous parabolic equation with subcritical nonlinearity

^e_\epsilon,f^e)\leqslant \hat{C}\beta(\epsilon). \end{array}$$ Proposition 25. Assume that ( H4 ) and (C) hold true and consider the family (Σ ε } ε∈[01] given in Definition 10 . Then we have that given sequences (ε n } n ∈ ℕ ⊂ (0,1] with ε n → 0+ and H n ∈ Σ ε n , for each n ∈ ℕ, there exists a convergent subsequence of (H n } n ∈ ℕ in (𝒞*, d*), with its limit belonging to Σ 0 . Proof. Since H n ∈ , item (b) of Lemma 12 implies that there exists λ n ∈ Γ ε n and h n ∈ 𝒢 εn such that Hn = B Xn h e n - A Xn , for each n e N. H n = B λ n

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Boundary value problems for fractional differential equation with causal operators

A. Wang G. 2012 Positive solutions of nonlinear fractional differential equations with integral boundary value conditions J. Math. Anal. Appl 389 403 411 doi 10.1016/j.jmaa.2011.11.065 [25] Y.Li.(2010), Solving a nonlinear fractional differential equation using Chebyshev wavelets. Commun.Nonlinear. Sci.Numer. Simul. 15, 2284-2292. 10.1016/j.cnsns.2009.09.020 Li Y. 2010 Solving a nonlinear fractional differential equation using Chebyshev wavelets. Commun.Nonlinear Sci.Numer. Simul 15 2284 2292 doi 10.1016/j.cnsns.2009.09.020 [26] Y.Zhao, S.Sun, Z.Han.(2011

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Multi-scale Simulations of Dry Friction Using Network Simulation Method

hydrodynamics bearings by the numerical network method Tribology International 40 1 139 145 10.1016/j.triboint.2006.03.008 [25] Benavent, A., Castro, E. et al. (2010). Evaluation of low-cycle fatigue damage in RC exterior beam-column subassemblages by acoustic emission. Construction and Building Materials 24: 1830-1842. 10.1016/j.conbuildmat.2010.04.021 Benavent A. Castro E. 2010 Evaluation of low-cycle fatigue damage in RC exterior beam-column subassemblages by acoustic emission Construction and Building Materials 24 1830 1842 10.1016/j.conbuildmat.2010.04.021 [26

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Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation

transform method [ 14 ], the Bäcklund transformation [ 15 ], the Darboux transformation [ 16 ], the Hirota bilinear method [ 17 ], the simplest equation method [ 18 ], the ( G ′/ G )–expansion method[ 19 , 20 ], the Jacobi elliptic function expansion method [ 21 ], the Kudryashov method [ 22 ], the Lie symmetry method [ 23 , 24 , 25 , 26 , 27 , 28 ]. The outline of the paper is as follows. In Section 2 we determine the travelling wave solutions for the system (2a) using the Lie symmetry method along with the ( G ′/ G )–expansion method. Conservation laws for (2a

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Multiple solutions of the Kirchhoff-type problem in RN

& {in{\rm{ \Omega }};} \hfill \\ {u = 0,} \hfill & {on{\rm{ }}\partial {\rm{\Omega }}} \hfill \\ \end{array}\right. \end{array}$$ (4) ( 4 ) is related to the stationary analogue of the equation u t t − ( a + b ) ∫ Ω | ▿ u | 2 d x ) ▵ u = g ( x , u ) $$\begin{array}{} \displaystyle {u_{tt}} - \left( {a + b} \right){\smallint _{\rm{\Omega }}}{\left| {\nabla u} \right|^2}dx)\Delta u = g\left( {x,u} \right) \end{array}$$ (5) which was proposed by Kirchhoff [ 2 ] as an extension of the classical D’Alembert’s wave equation for free vibrations of elastic

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Analytical solutions of the relative orbital motion in unperturbed and in J 2 - perturbed elliptic orbits

Conference Ponce, Puerto Rico, No. AAS 03-138 [9] Wiesel, W. E.,(1989), Spaceight Dynamics, McGraw-Hill, Inc., New York. Wiesel W. E. 1989 Spaceight Dynamics McGraw-Hill, Inc. New York [10] Schweighart, S. A., and Sedwick, R. J. (2002). High-Fidelity Linearized J 2 Model for Satellite Formation Flight. Journal of Guidance, Control and Dynamics, Vol.25, No.6, pp. 1073–1080. 10.2514/2.4986 Schweighart S. A. Sedwick R. J. 2002 High-Fidelity Linearized J 2 Model for Satellite Formation Flight Journal of Guidance, Control and Dynamics Vol.25 No.6 pp. 1073 1080 [11

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Effects of second-order slip and drag reduction in boundary layer flows

to be β > β c , where β ≈ 2.5. For computational purposes, we set β = 3 and minimize the error function (26) to obtain the optimal value of ℏ . We consider the following three sets of values for the parameters: Mn = 15, C = 0.001, λ 1 = 0.3, γ = 1.0, and δ = –2.0, Mn = 20, C = 0.01, λ 1 = 0.2, γ = 0.5, and δ = –0.5, Mn = 10, C = 0.1, λ 1 = 0.1, γ = 0.1, and δ = –1.0, and calculate the 10 th -order HAM solution with β = 3. The optimal values for the convergence control parameter ℏ are found to be, I

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The effect of two-temperature on thermoelastic medium with diffusion due to three phase-lag model

, ρ = 8954 k g / m 3 , λ = 7.76 × 10 10 k g / ( m . s 2 ) , μ = 3.86 × 10 10 k g / ( m . s 2 ) , α c = 1.98 × 10 − 4 m 3 / k g , K = 300 W , d = 0.85 × 10 − 8 k g . s / m 3 , a = 1.2 × 10 4 m 2 / ( s 2 . K ) , b 1 = 0.9 × 10 6 m 5 / ( k g . s 2 ) , ω o = 2.5 , ξ = 0.4 , ω = ω o + i ξ , x = 0.5 , t = 0.2 , K * = 2.97 × 10 13 , k = 2.4 , p = 0.1 , b = 0.2 , τ v = 0.2 , τ T = 0.5 , τ q = 0.8. $$\begin{array}{} \begin{array}{*{20}{c}} {{T_o} = 293K,{C_E} = 383.1J/(kg.K),{\alpha _t} = 1.78 \times {{10}^{ - 5}}{K^{ - 1}},\rho = 8954kg/{m^3},\lambda = 7.76 \times {{10

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