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1.
Using the abstract framework [Bátkai, A. and Engel, K.-J., 2004, Abstract wave equations with generalized Wentzell boundary conditions. Journal of Differential Equations, 207, 1–20.] we show that certain second-order differential operators with generalized Wentzell boundary conditions generate cosine families and hence also analytic semigroups on W1,1(0,1). This complements the main result [Favini, A., Ruiz Goldstein, G., Goldstein, J.A., Obrecht, E. and Romanelli, S., 2003, General Wentzell boundary conditions and analytic semigroups on W1, p (0,1). Applicable Analysis, 82, 927–935.] on the generation of an analytic semigroup by the second derivative with generalized Wentzell boundary conditions on W1, p (0,?1) for 1<p<∞.  相似文献   

2.
Existence conditions for interpolation problems of the Pick-Nevanlinna and Loewner types are discussed in the case of operator valued functions.Supported by NSF Grant MCS 81-02518. The second author also acknowledges support from the Alexander von Humboldt Foundation and generous hospitality from the Rhein.-Westf. Techn. Hochschule Aachen and Universität Tübingen.  相似文献   

3.
** Email: David.Cohen{at}math.unige.ch. Present address: Mathematisches Institut, Universität Tübingen, D-72076 Tübingen, Germany (cohen{at}na.uni-tuebingen.de) Modulated Fourier expansion is used to show long-time near-conservationof the total and oscillatory energies of numerical methods forHamiltonian systems with highly oscillatory solutions. The numericalmethods considered are an extension of the trigonometric methods.A brief discussion of conservation properties in the continuousproblem and in the multi-frequency case is also given.  相似文献   

4.
We introduce a general framework which allows to verify if abstract wave equations with generalized Wentzell boundary conditions are well-posed, i.e., are governed by a cosine family. As an example we study wave equations for second order differential operators on C[0,1] with non-local Wentzell-type boundary conditions. Moreover, in Appendix A we give a perturbation result for sine and cosine families.  相似文献   

5.
In this paper we consider a semilinear equation with a generalized Wentzell boundary condition. We prove the local well-posedness of the problem and derive the conditions of the global existence of the solution and the conditions for finite time blow-up. We also derive an estimate for the blow-up time.  相似文献   

6.
We are concerned with linear wave equations with Wentzell boundary conditions of dynamical type, where only one velocity feedback force acts on the Wentzell boundary. By using the theory of strongly continuous semigroups of linear operators, we prove that the energies of the solutions are strongly stable. Moreover, we show in the one dimensional case that there are solutions decaying at arbitrarily slow rates.  相似文献   

7.
We introduce a general framework to treat abstract quasilinear equations of second order with Wentzell boundary conditions. As an example we study a wave equation for a second order quasilinear differential operator on with Wentzell boundary conditions.  相似文献   

8.
Elliptic boundary value problems with analytic functionals as data have been studied by Lions and Magenes. In this papér we relax their assumption that the boundary of the domain ω is an analytic surface; we assume only that ω equals the interior of its closure. In this case we obtain results for the Dirichlet problem for second order equations that are analogous to theirs: There is a quasi-analytic class of functions on0ω with a natural topology such that the Dirichlet problem is well posed the data belongs to the dual of this space. The author acknowledges with gratitude the support he received from the National Science Foundation through a graduate fellowship and NSFGP 6761. Entrata in redazione il 31 gennaio 1969  相似文献   

9.
In this paper, we study the nonautonomous heat equation in C[0,1] C[0,1] with generalized Wentzell boundary conditions.It is shown, under appropriate assumptions, that there exists a unique evolution family for this problem and that the family satisfies various regularity properties. This enables us to obtain, for the corresponding inhomogeneous problem, classical and strict solutions having optimal regularity.  相似文献   

10.
The set of Nash equilibria is computed for some generalized games. It is also studied for a subclass of standardn-person games.The authors acknowledge the support of CONICET (Consejo de Investigaciones Cientificas y Tecnicas de la Republica Argentina). The first author acknowledges the support from TWAS (Third World Academy of Sciences), Grant No. 86-33.  相似文献   

11.
Boundary control problems for quasi-linear elliptic equations:   总被引:1,自引:0,他引:1  
In this paper we prove some optimality conditions, in the form of a Pontryagin's principle, for boundary control problems governed by quasi-linear elliptic equations. Because of the presence of state constraints, we distinguish the cases of qualified and nonqualified conditions for optimality. Both cases are treated in the paper. Neither convexity of the control set nor differentiability of the functions involved in the control problem are assumed.This research was partially supported by Dirección General de Investigation Científica y Técnica (Madrid).  相似文献   

12.
In this paper,we study mixed elastico-plasticity problems in which part of the boundary is known,while the other part of the boundary is unknown and is a free boundary.Under certain conditions,this problemcan be transformed into a Riemann-Hilbert boundary value problem for analytic functions and a mixed boundaryvalue problem for complex equations.Using the theory of generalized analytic functions,the solvability of theproblem is discussed.  相似文献   

13.
Of concern are the initial-boundary value problems for nonautonomous semilinear second order evolution equations with generalized Wentzell boundary conditions. We succeed in establishing a global wellposedness theorem (in a classical sense) for these problems via a specifically designed operator theoretic approach. Moreover, we obtain sharp estimations for the evolution of the solution along the characteristic curves, which enable us to derive the uniform exponential decay of the associated energies. The results obtained in this paper are still new even for the autonomous case.  相似文献   

14.
The present work deals with the formulation of the boundary integral equations for the solution of equations under linear theory of generalized thermoelastic diffusion in a three-dimensional Euclidean space. A mixed initial-boundary value problem is considered in the present context and the fundamental solutions of the corresponding coupled differential equations are obtained in the Laplace transform domain by employing the treatment of scalar and vector potential theory. A reciprocal relation of Betti type is established. Then we formulate the boundary integral equations for generalized thermoelastic diffusion on the basis of these fundamental solutions and the reciprocal relation.  相似文献   

15.
This paper is concerned with the existence and uniqueness of solutions to first-order linear differential equations of neutral type with a nonatomicD-operator. We use an algebraic approach, in the context of the theory of convolution operators. Necessary and sufficient conditions are given for the initial value problem to have unique solutions for a class of equations.This work was done while the author was at the Department of Mathematics, Virginia Polytechnic Institute and State University.Instituto de Desarrollo Tecnológico para la Industria Quimica (INTEC), dependent on Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) and the Universidad Nacional del Litoral (UNL).  相似文献   

16.
The Hamiltonian formulation of the Einstein equations is achieved by means of a foliation of the background Lorentz Manifold. The usage of maximal surfaces is the frequently applied gauge for numerical research of asymptotically flat manifolds. In this paper we construct a foliation of asymptotically hyperbolic 3-surfaces through 2-surfaces (with constant mean curvature) homeomorphic to spheres. This is established by using the volume preserving mean curvature flow. These spheres define a geometric intrinsic radius coordinate near infinity and therefore define a center of mass for the Bondi case.This paper was founded by the Deutschen Foschungsgemeinschaft, Sonderforschungsbereich 382 of the Universities Tübingen and Stuttgart.  相似文献   

17.
Using the method of contracting mappings, we prove, for small values of time, the existence and uniqueness of a generalized Lipschitz solution of a mixed problem with unknown boundaries for a hyperbolic quasilinear system of first-order equations represented in terms of Riemann invariants with nonlocal (nonseparated and integral) boundary conditions.  相似文献   

18.
A mixed boundary-value problem for the nonlinear Schrödinger equation and its generalization is studied by the method used for the inverse scattering problem. A connection is established between conservation laws and boundary conditions in integrable boundary-value problems for higher nonlinear Schrödinger equations. It is shown that the generalized boundary-value problem requires a joint consideration of regular and singular solutions for the nonlinear Schrödinger equation with repulsion.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 151–165, 1988.  相似文献   

19.
20.
The Euler-Korteweg system is a third order, dispersive system of PDEs, obtained from the standard Euler equations for compressible fluids by adding the so-called Korteweg stress tensor - encoding capillarity effects. Various results of well-posedness have been obtained recently for the Cauchy problem associated with the Euler-Korteweg system in the whole space. As to mixed problems, with initial and boundary value data, they are still mostly open. Here the linearized Euler-Korteweg system is studied in a half space by the use of normal mode analysis, which yields a generalized Kreiss-Lopatinski? condition that must be satisfied by the boundary conditions for the boundary value problem to be well-posed.Conversely, under the uniform Kreiss-Lopatinski? condition, generalized Kreiss symmetrizers are constructed in one space dimension for an extended system originally introduced for the Cauchy problem, which displays crucial quasi-homogeneity properties. A priori estimates without loss of derivatives are thus derived, and finally the well-posedness of the mixed problem is obtained by combining the estimates for the pure boundary value problem and trace results for solutions of the pure Cauchy problem.  相似文献   

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