On a unique recovery of lower-order terms in the wave equation from dynamical boundary measurements

2000 ◽  
Vol 101 (5) ◽  
pp. 3408-3421 ◽  
Author(s):  
M. I. Belishev
Keyword(s):  
Wave Equation ◽  
Lower Order ◽  
Boundary Measurements ◽  
Lower Order Terms

scholarly journals The exponential stability of the problem of transmission of the wave equation

1998 ◽  
Vol 57 (2) ◽  
pp. 305-327 ◽  
Author(s):  
Weijiu Liu ◽  
Graham Williams
Keyword(s):  
Wave Equation ◽  
Exponential Stability ◽  
Energy Method ◽  
Lower Order ◽  
Classical Energy ◽  
Exponentially Stable ◽  
Lower Order Terms

The problem of exponential stability of the problem of transmission of the wave equation with lower-order terms is considered. Making use of the classical energy method and multiplier technique, we prove that this problem of transmission is exponentially stable.

scholarly journals Nonlinear evolution problems with singular coefficients in the lower order terms

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Fernando Farroni ◽  
Luigi Greco ◽  
Gioconda Moscariello ◽  
Gabriella Zecca
Keyword(s):  
Lower Order ◽  
Time Horizon ◽  
Existence Result ◽  
Nonlinear Evolution ◽  
Order Term ◽  
Time Behavior ◽  
Infinite Time ◽  
Singular Coefficient ◽  
Singular Coefficients ◽  
Lower Order Terms

AbstractWe consider a Cauchy–Dirichlet problem for a quasilinear second order parabolic equation with lower order term driven by a singular coefficient. We establish an existence result to such a problem and we describe the time behavior of the solution in the case of the infinite–time horizon.

scholarly journals Existence results for nonlinear degenerate elliptic equations with lower order terms

2020 ◽  
Vol 10 (1) ◽  
pp. 301-310
Author(s):  
Weilin Zou ◽  
Xinxin Li
Keyword(s):  
Lower Order ◽  
Elliptic Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Regularity Of Solutions ◽  
Degenerate Elliptic Equations ◽  
Degenerate Elliptic ◽  
Initial Boundary Value ◽  
Lower Order Terms ◽  
Nonlinear Degenerate

Abstract In this paper, we prove the existence and regularity of solutions of the homogeneous Dirichlet initial-boundary value problem for a class of degenerate elliptic equations with lower order terms. The results we obtained here, extend some existing ones of [2, 9, 11] in some sense.

Zero correlation with lower-order terms for automorphic L-functions

2016 ◽  
Vol 12 (01) ◽  
pp. 27-55
Author(s):  
Timothy L. Gillespie ◽  
Yangbo Ye
Keyword(s):  
Lower Order ◽  
Product Formula ◽  
Cuspidal Representation ◽  
Zero Correlation ◽  
Lower Order Terms ◽  
Refined Version ◽  
Low Order

Let [Formula: see text] be a self-contragredient automorphic cuspidal representation of [Formula: see text] for [Formula: see text]. Using a refined version of the Selberg orthogonality, we recompute the [Formula: see text]-level correlation of high non-trivial zeros of the product [Formula: see text]. In the process, we are able to extract certain low-order terms which suggest the asymptotics of these statistics are not necessarily universal, but depend upon the conductors of the representations and hence the ramification properties of the local components coming from each [Formula: see text]. The computation of these lower-order terms is unconditional as long as all [Formula: see text].

scholarly journals Tight Bounds for Quasirandom Rumor Spreading

10.37236/191 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Spyros Angelopoulos ◽  
Benjamin Doerr ◽  
Anna Huber ◽  
Konstantinos Panagiotou
Keyword(s):  
Lower Order ◽  
Fundamental Problem ◽  
Classical Approach ◽  
Rumor Spreading ◽  
The People ◽  
Single Person ◽  
Group Members ◽  
Short Time ◽  
Push Model ◽  
Lower Order Terms

This paper addresses the following fundamental problem: Suppose that in a group of $n$ people, where each person knows all other group members, a single person holds a piece of information that must be disseminated to everybody within the group. How should the people propagate the information so that after short time everyone is informed? The classical approach, known as the push model, requires that in each round, every informed person selects some other person in the group at random, whom it then informs. In a different model, known as the quasirandom push model, each person maintains a cyclic list, i.e., permutation, of all members in the group (for instance, a contact list of persons). Once a person is informed, it chooses a random member in its own list, and from that point onwards, it informs a new person per round, in the order dictated by the list. In this paper we show that with probability $1-o(1)$ the quasirandom protocol informs everybody in $(1 \pm o(1))\log_2 n+\ln n$ rounds; furthermore we also show that this bound is tight. This result, together with previous work on the randomized push model, demonstrates that irrespectively of the choice of lists, quasirandom broadcasting is as fast as broadcasting in the randomized push model, up to lower order terms. At the same time it reduces the number of random bits from $O(\log^2 n)$ to only $\lceil\log_2 n\rceil$ per person.

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