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Träfflista för sökning "LAR1:cth ;lar1:(gu);lar1:(cth);pers:(Svanstedt Nils 1958)"

Sökning: LAR1:cth > Göteborgs universitet > Chalmers tekniska högskola > Svanstedt Nils 1958

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11.
  • Nguetseng, Gabriel, et al. (författare)
  • G-Convergence and Homogenization of Monotone Damped Hyperbolic Equations
  • 2010
  • Ingår i: Banach Journal of Mathematical Analysis. - 1735-8787. ; 4:1, s. 100-115
  • Konferensbidrag (refereegranskat)abstract
    • Multiscale stochastic homogenization is studied for quasilinear hyperbolic problems. We consider the asymptotic behaviour of a sequence of realizations of the form partial derivative(2)u(epsilon)(omega)/partial derivative t(2) - div (a(T(1)(x/epsilon(1))omega(1), T(2)(x/epsilon(2))omega(2), t, Du(epsilon)(omega))) - Delta(partial derivative u(epsilon)(omega)/partial derivative t) + G(T(3)(x/epsilon(3))omega(3,) t, partial derivative u(epsilon)(omega)/partial derivative t) = f. It is shown, under certain structure assumptions on the random maps a(omega(1), omega(2,) t, xi) and G(omega(3), t, eta), that the sequence {u(epsilon)(omega)} of solutions converges weakly in L(p)(0, T; W(0)(1,p)(Omega)) to the solution u of the homogenized problem partial derivative(2)u/partial derivative t(2) - div (b(t, (Du)) - Delta(partial derivative u/partial derivative t) + (G) over bar (t, partial derivative u/partial derivative t) = f.
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12.
  • Nguetseng, Gabriel, et al. (författare)
  • Sigma-convergence
  • 2010
  • Annan publikation (övrigt vetenskapligt/konstnärligt)
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13.
  • Nguetseng, G, et al. (författare)
  • Sigma-CONVERGENCE
  • 2011
  • Ingår i: BANACH JOURNAL OF MATHEMATICAL ANALYSIS. - 1735-8787. ; 5:1, s. 101-135
  • Tidskriftsartikel (refereegranskat)abstract
    • We discuss two new concepts of convergence in Lp-spaces, the socalled weak-convergence and strong convergence, which are intermediate between classical weak convergence and strong convergence. We also introduce the concept of -convergence for Radon measures. Our basic tool is the classical Gelfand representation theory. Apart from being a natural generalization of well-known two-scale convergence theory, the present study lays the foundation of the mathematical framework that is needed to undertake a systematic study of deterministic homogenization problems beyond the usual periodic setting. A few homogenization problems are worked out by way of illustration.
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16.
  • Sango, M, et al. (författare)
  • Generalized Besicovitch spaces and applications to deterministic homogenization
  • 2011
  • Ingår i: Nonlinear Analysis: Theory, Methods & Applications. - : Elsevier BV. - 0362-546X. ; 74:2, s. 351-379
  • Tidskriftsartikel (refereegranskat)abstract
    • The purpose of the present work is to introduce a framework which enables us to study nonlinear homogenization problems. The starting point is the theory of algebras with mean value. Very often in physics, from very simple experimental data, one gets complicated structure phenomena. These phenomena are represented by functions which are permanent in mean, but complicated in detail. In addition the functions are subject to the verification of a functional equation which in general is nonlinear. The problem is therefore to give an interpretation of these phenomena using functions having the following qualitative properties: they are functions that represent a phenomenon on a large scale, and which vary irregularly, undergoing nonperiodic oscillations on a fine scale. In this work we study the qualitative properties of spaces of such functions, which we call generalized Besicovitch spaces, and we prove general compactness results related to these spaces. We then apply these results in order to study some new homogenization problems. One important achievement of this work is the resolution of the generalized weakly almost periodic homogenization problem for a nonlinear pseudo-monotone parabolic-type operator. We also give the answer to the question raised by Frid and Silva in their paper [35] [H. Frid, J. Silva, Homogenization of nonlinear pde’s in the Fourier–Stieltjes algebras, SIAM J. Math. Anal, 41 (4) (2009) 1589–1620] as regards whether there exist or do not exist ergodic algebras that are not subalgebras of the Fourier–Stieltjes algebra.
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18.
  • Svanstedt, Nils, 1958, et al. (författare)
  • A one-population Amari model with periodic microstructure
  • 2014
  • Ingår i: Nonlinearity. - : IOP Publishing. - 0951-7715 .- 1361-6544. ; 27:6, s. 1391-1417
  • Tidskriftsartikel (refereegranskat)abstract
    • We review the derivation of the homogenized one- population Amari equation by means of the two-scale convergence technique of Nguetseng in the case of periodic microvariation in the connectivity function. A key point in this derivation is Visintin's theorem for two-scale convergence of convolution integrals. We construct single bump solutions of the resulting homogenized equation using a pinning function technique for the case where the solutions are independent of the local variable and the firing rate function is modelled as a unit step function. The parameter measuring the degree of heterogeneity plays the role of a control parameter. The connectivity functions are periodically modulated in both the synaptic footprint and in the spatial scale. A framework for analysing the stability of these structures is formulated. This framework is based on spectral theory for Hilbert-Schmidt integral operators and it deforms to the standard Evans function approach for the translational invariant case in the limit of no heterogeneity. The upper and lower bounds of the growth/decay rates of the perturbations imposed on the bump states can be expressed in terms of the operator norm of the actual Hilbert- Schmidt operator. Intervals for which the pinning function is increasing correspond to unstable bumps, while complementary intervals where the pinning function decreases correspond to stable bumps, just as in the translational invariant case. Examples showing the properties of the bumps are discussed in detail when the connectivity kernels are given in terms of an exponential decaying function, a wizard hat function and a damped oscillating function.
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  • Resultat 11-20 av 32

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