In this paper we consider the inverse problem of recovering the viscosity coefficient in a dissipative wave equation via boundary measurements. We obtain stability estimates by considering all possible measurements implemented on the boundary. We also prove that the viscosity coefficient is uniquely determined by a finite number of measurements on the boundary provided that it belongs to a given finite dimensional vector space.  2005 Elsevier Inc. All rights reserved.

In this paper, we investigate the existence and uniqueness of a solution for differential equations of the carrier type on lateral boundary † of the cylinder Q, cf. (1). The main point is to transform this initial value problem into a differential operator equation of the type u 00 C M ÂZ cf. (6). The operator A is defined in Section 2, and it acts in Sobolev spaces on , boundary of . The initial value problem (6) is investigated in Section 3 by the method of Faedo-Galerkin. Thus, we obtain the existence of a weak solution for (6), and in Section 4, we prove its uniqueness.Ã Au Cˇu 0ˇ u 0 D f , and we can apply the usual methodology for the initial value problem (6).

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In this work we investigate the existence and the uniqueness of solution for a nonlinear differential equation of parabolic type on the lateral boundary Σ of a cylinder Q, cf. (1). An important part of our study is to transform this initial value problem into another one whose differential operator equation is of the typecf. (9), where k is a positive integer. The operator A acts in Sobolev spaces on Γ, boundary of Ω. The initial value problem (9) will be studied in Section 4. Thus, we obtain the existence and the uniqueness of weak solution for (9).

ABSTRACT. In this paper we investigate the existence of solution for an initial boundary value problem of the following nonlinear wave equation:where Q represents a non-cylindrical domain of R n+1 . The methodology, cf. Lions [3], consists of transforming this problem, by means of a perturbation depending on a parameter ε > 0, into another one defined in a cylindrical domain Q containing Q. By solving the cylindrical problem, we obtain estimates that depend on ε. These ones will enable a passage to the limit, when ε goes to zero, that will guarantee, later, a solution for the non-cylindrical problem. The nonlinearity |u ε | ρ introduces some obstacles in the process of obtaining a priori estimates and we overcome this difficulty by employing an argument due to Tartar [8] plus a contradiction process.