The diffusion equation in a notched beam

Casado-Díaz, Juan; Luna-Laynez, Manuel; Murat, François
March 2008
Calculus of Variations & Partial Differential Equations;Mar2008, Vol. 31 Issue 3, p297
Academic Journal
We study the asymptotic behavior of the solution of a diffusion problem posed in a beam with a notch. We give an approximation in the L 2 strong topology of this solution and of its gradient (corrector result) according to the size of the notch.


Related Articles

  • On the accuracy of the normal approximation for sums of symmetric independent random variables. Shevtsova, I. // Doklady Mathematics;Apr2012, Vol. 85 Issue 2, p292 

    The article focuses on the accuracy of normal approximation for the sums of symmetric independent random variables. It states that a new asymptotic error estimates of the normal approximation for sums of independent random variables with arbitrary distributions having finite third moments were...

  • Numerical quenching for a nonlinear diffusion equation with a singular boundary condition. Nabongo, Diabate; Boni, Th�odore K. // Bulletin of the Belgian Mathematical Society - Simon Stevin;May2009, Vol. 16 Issue 2, p289 

    This paper concerns the study of the numerical approximation for the following boundary value problem { (um)t = uxx, 0 < x < 1, t > 0, ux(0, t) = 0, ux(1, t) = -u-�(1, t), t > 0, u(x, 0) = u0(x) > 0, 0 = x = 1, where m = 1, � > 0. We obtain some conditions under which the solution of a...

  • Asymptotic optimization for stochastic models based on a compound poisson process. Voina, A. A. // Cybernetics & Systems Analysis;Jul2011, Vol. 47 Issue 4, p649 

    This paper considers the possibility of using a multidimensional compound Poisson process controlled by a continuous-time Markov chain in mathematical decision-making models. A definition of this process is presented and examples are given that illustrate its use in formalizing the concepts of...

  • Dynamics of quantum discord in two Tavis-Cummings models with classical driving fields. Zhang, Y.; Xu, J. // European Physical Journal D -- Atoms, Molecules, Clusters & Opti;Oct2011, Vol. 64 Issue 2/3, p549 

    We investigate the dynamics of quantum discord in a system consisting of two Tavis-Cummings models, each of which contains two atoms driven by a classical field. We compare the dynamics of quantum discord for the system with that of entanglement and show that quantum discord vanishes only...

  • A random energy model for size dependence: recurrence vs. transience. Külske, Christof // Probability Theory & Related Fields;1998, Vol. 111 Issue 1, p57 

    Summary. We investigate the size dependence of disordered spin models having an infinite number of Gibbs measures in the framework of a simplified 'random energy model for size dependence'. We introduce two versions (involving either independent random walks or branching processes), that can be...

  • Rescaled contact processes converge to super-Brownian motion in two or more dimensions. Durrett, Richard; Perkins, Edwin A. // Probability Theory & Related Fields;1999, Vol. 114 Issue 3, p309 

    Abstract. We show that in dimensions two or more a sequence of long range contact processes suitably rescaled in space and time converges to a super-Brownian motion with drift. As a consequence of this result we can improve the results of Bramson, Durrett, and Swindle (1989) by replacing their...

  • The Piltz's problem over a ring of matrices of second order with integer elements. Velichko, Igor // Journal of Mathematical Sciences;Jul2013, Vol. 192 Issue 4, p459 

    The asymptotic formula for a summatory function of the number of representations of matrices from $ {M_2}\left( \mathbb{Z} \right) $ in the form C = A A A under the condition det C ≤ x is constructed. The second moment of the error term of this asymptotic formula is estimated.

  • Allocation of Service Time in a Multiserver System. El-Taha, Muhammad; Maddah, Bacel // Management Science;Apr2006, Vol. 52 Issue 4, p623 

    Reducing congestion is a primary concern in the design and analysis of queueing networks, especially in systems where sources of randomness are characterized by high variability. This paper considers a multiserver first-come, first-served (FCFS) queueing model where we arrange servers in two...

  • Refining the Diffusion Approximation for the M/G/m Queue. Yao, David D. // Operations Research;Nov/Dec85, Vol. 33 Issue 6, p1266 

    Despite its many and varied applications, the M/G/m queue has yet to be solved exactly. Consequently, researchers have developed many methods for approximating its solution. We refine a diffusion approximation model developed by Kimura for the M/G/m queue, using an alternative approach to...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics