The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform
Yanni Zeng - One of the best experts on this subject based on the ideXlab platform.
-
LARGE TIME BEHAVIOR OF SOLUTIONS TO NONLINEAR VISCOELASTIC MODEL WITH Fading Memory
Acta Mathematica Scientia, 2012Co-Authors: Yanni ZengAbstract:Abstract We study the Cauchy problem of a one-dimensional nonlinear viscoelastic model with Fading Memory. By introducing appropriate new variables we convert the integro-partial differential equations into a hyperbolic system of balance laws. When it is a perturbation of a constant state, the solution is shown time asymptotically approaching to predetermined diffusion waves. Pointwise estimates on the convergence details are obtained.
-
Convergence to diffusion waves of solutions to nonlinear viscoelastic model with Fading Memory
Communications in Mathematical Physics, 1992Co-Authors: Yanni ZengAbstract:We study the large time behavior inL2 of solutions to a model for the motion of an unbounded, homogeneous, viscoelastic bar with Fading Memory. Decay rates for the solutions are obtained under the assumption that the initial data and histories are smooth and small. Moreover, convergence of the solutions to diffusion waves, which are solutions of Burgers equations, is proved and rates are obtained. Our method is based on the study of properties of the solutions to the linearized system in the Fourier space.
Catherine Marquet - One of the best experts on this subject based on the ideXlab platform.
-
Ergodic and weighted pseudo-almost periodic solutions for partial functional differential equations in Fading Memory spaces
Journal of Applied Mathematics and Computing, 2014Co-Authors: Mostafa Adimy, Khalil Ezzinbi, Catherine MarquetAbstract:We use a new concept of weighted ergodic function based on the measure theory to investigate the existence and uniqueness of weighted pseudo almost periodic solution for a class of partial functional differential equations with infinite delay in Fading Memory spaces. We illustrate our theoretical results by studying some Lotka-Voltera reaction-diffusion systems with infinite delay.
-
Ergodic and weighted pseudo-almost periodic solutions for partial functional differential equations in Fading Memory spaces
Journal of Applied Mathematics and Computing, 2013Co-Authors: Mostafa Adimy, Khalil Ezzinbi, Catherine MarquetAbstract:International audienceWe use a new concept of weighted ergodic function based on the measure theory to investigate the existence and uniqueness of weighted pseudo almost periodic solution for a class of partial functional differential equations with infinite delay in Fading Memory spaces. We illustrate our theoretical results by studying some Lotka-Voltera reaction-diffusion systems with infinite delay
Richard J. Loy - One of the best experts on this subject based on the ideXlab platform.
-
rheological implications of completely monotone Fading Memory
Journal of Rheology, 2002Co-Authors: Robert S. Anderssen, Richard J. LoyAbstract:In the constitutive equation modeling of a (linear) viscoelastic material, the “Fading Memory” of the relaxation modulus G(t) is a fundamental concept that dates back to Boltzmann [Ann. Phys. Chem. 7, 624 (1876)]. There have been various proposals that range from the experimental and pragmatic to the theoretical about how Fading Memory should be defined. However, if, as is common in the rheological literature, one assumes that G(t) has the following relaxation spectrum representation: G(t)=∫0∞ exp(−t/τ)[H(τ)/τ]dτ, t > 0, then it follows automatically that G(t) is a completely monotone function. Such functions have quite deep mathematical properties, that, in a rheological context, spawn interesting and novel implications. For example, because the set of completely monotone functions is closed under positive linear combinations and products, it follows that the dynamics of a linear viscoelastic material, under appropriate stress–strain stimuli, will involve a simultaneous mixture of different molecular interactions. In fact, it has been established experimentally, for both binary and polydisperse polymeric systems, that the dynamics can simultaneously involve a number of different molecular interactions such as the Rouse, double reptation and/or diffusion, [W. Thimm et al., J. Rheol., 44, 429 (2000); F. Leonardi et al., J. Rheol. 44, 675 (2000)]. The properties of completely monotone functions either yield new insight into modeling of the dynamics of real polymers, or they call into question some of the key assumptions on which the current modeling is based, such as the linearity of the Boltzmann model of viscoelasticity and/or the relaxation spectrum representation for the relaxation modulus G(t). If the validity of the relaxation spectrum representation is accepted, the resulting mathematical properties that follow from the complete monotonicity of G(t) allows one to place the classical relaxation model of Doi and Edwards [M. Doi and S. F. Edwards, J. Chem. Soc., Faraday Trans. 2 74, 1789 (1978)], as a linear combination of exp(−t/τ*) relaxation processes, each with a characteristic relaxation time τ*, on a more general and rigorous footing.
-
completely monotone Fading Memory relaxation modulii
Bulletin of The Australian Mathematical Society, 2002Co-Authors: Robert S. Anderssen, Richard J. LoyAbstract:J—oo which defines how the stress a(t) at time t depends on the earlier history of the shear rate j(r) via the relaxation modulus (kernel) G(t). Physical reality is achieved by requiring that the form of the relaxation modulus G(t) gives the Boltzmann equation Fading Memory, so that changes in the distant past have less effect now than the same changes in the more recent past. A popular choice, though others have previously been proposed and investigated, is the assumption that G(t) be a completely monotone function. This assumption has much deeper ramifications than have been identified, discussed or exploited in the rheological literature. The purpose of this paper is to review the key mathematical properties of completely monotone functions, and to illustrate how these properties impact on the theory and application of linear viscoelasticity and polymer dynamics. A more general representation of a completely monotone function, known in the mathematical literature, but not the rheological, is formulated and discussed. This representation is used to derive new rheological relationships. In particular, explicit inversion formulas are derived for the relationships that are obtained when the relaxation spectrum model and a mixing rule are linked through a common relaxation modulus.
-
Rheological implications of completely monotone Fading Memory
Journal of Rheology, 2002Co-Authors: Robert S. Anderssen, Richard J. LoyAbstract:In the constitutive equation modeling of a (linear) viscoelastic material, the “Fading Memory” of the relaxation modulus G(t) is a fundamental concept that dates back to Boltzmann [Ann. Phys. Chem. 7, 624 (1876)]. There have been various proposals that range from the experimental and pragmatic to the theoretical about how Fading Memory should be defined. However, if, as is common in the rheological literature, one assumes that G(t) has the following relaxation spectrum representation: G(t)=∫0∞ exp(−t/τ)[H(τ)/τ]dτ, t > 0, then it follows automatically that G(t) is a completely monotone function. Such functions have quite deep mathematical properties, that, in a rheological context, spawn interesting and novel implications. For example, because the set of completely monotone functions is closed under positive linear combinations and products, it follows that the dynamics of a linear viscoelastic material, under appropriate stress–strain stimuli, will involve a simultaneous mixture of different molecular int...
Khalil Ezzinbi - One of the best experts on this subject based on the ideXlab platform.
-
Ergodic and weighted pseudo-almost periodic solutions for partial functional differential equations in Fading Memory spaces
Journal of Applied Mathematics and Computing, 2014Co-Authors: Mostafa Adimy, Khalil Ezzinbi, Catherine MarquetAbstract:We use a new concept of weighted ergodic function based on the measure theory to investigate the existence and uniqueness of weighted pseudo almost periodic solution for a class of partial functional differential equations with infinite delay in Fading Memory spaces. We illustrate our theoretical results by studying some Lotka-Voltera reaction-diffusion systems with infinite delay.
-
Ergodic and weighted pseudo-almost periodic solutions for partial functional differential equations in Fading Memory spaces
Journal of Applied Mathematics and Computing, 2013Co-Authors: Mostafa Adimy, Khalil Ezzinbi, Catherine MarquetAbstract:International audienceWe use a new concept of weighted ergodic function based on the measure theory to investigate the existence and uniqueness of weighted pseudo almost periodic solution for a class of partial functional differential equations with infinite delay in Fading Memory spaces. We illustrate our theoretical results by studying some Lotka-Voltera reaction-diffusion systems with infinite delay
-
Periodic solutions in Fading Memory spaces
2005Co-Authors: Khalil Ezzinbi, Nguyen Van MinhAbstract:For $A(t)$ and $f(t,x,y)$ $T$-periodic in $t$, consider the following evolution equation with infinite delay in a general Banach space $X$, $$u^\prime (t)+ A(t)u(t)=f(t,u(t),u_t),\;\; t> 0,\;\;u(s) =\phi (s),\;\;s \leq 0, $$ where the resolvent of the unbounded operator $A(t)$ is compact, and $u_t (s)=u(t+s),\; s\leq 0$. We will work with general Fading Memory phase spaces satisfying certain axioms, and derive periodic solutions. We will show that the related Poincar\'{e} operator is condensing, and then derive periodic solutions using the boundedness of the solutions and some fixed point theorems. This way, the study of periodic solutions for equations with infinite delay in general Banach spaces can be carried to Fading Memory phase spaces. In doing so, we will improve a condition of [4] and extend the results of [7,8].
John N. Tsitsiklis - One of the best experts on this subject based on the ideXlab platform.
-
Worst-case identification of nonlinear Fading Memory systems
Automatica, 1995Co-Authors: Munther A. Dahleh, Eduardo D. Sontag, David Tse, John N. TsitsiklisAbstract:Abstract In this paper, the problem of asymptotic identification for Fading Memory systems in the presence of bounded noise is studied. For any experiment, the worst-case error is characterized in terms of the diameter of the worst-case uncertainty set. Optimal inputs that minimize the radius of uncertainty are studied and characterized. Finally, a convergent algorithm that does not require knowledge of the noise upper bound is furnished. The algorithm is based on interpolating data with spline functions, which are shown to be well suited for identification in the presence of bounded noise—more so than other basis functions such as polynomials.
-
Worst-Case Identification of Nonlinear Fading Memory Systems
1992 American Control Conference, 1992Co-Authors: Munther A. Dahleh, Eduardo D. Sontag, David Tse, John N. TsitsiklisAbstract:In this paper, the problem of asymptotic identification for a class of nonlinear Fading Memory systems in the presence of bounded noise is studied. For any experiment, the worst-case error is characterized in terms of the diameter of the worst-case uncertainty set. Optimal inputs that minimize the radius of uncertainty are studied and characterized. Finally, a convergent algorithm that does not require knowledge of the noise upper bound is furnished. The methods as well as the results are quite general and are applicable to a larger variety of settings.
