摘要:

AbstractA one dimensional problem forSHwaves in an elastic medium is treated which can be written asvtt=A−1(Avy)y,A= (ϱμ)1/2, ϱ = density, and μ = shear modulus. AssumeAϵC1andA′/AϵL1; from an inputvy(t, 0) = ∂(t) let the responsev(t, 0) =g(t) be measured (v(t, y) = 0 fort0 in terms of the solutionKof a Gelfand‐Levitan ty

ISSN:0170-4214    

DOI:10.1002/mma.1670030112

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractA new asymptotic expansion algorithm related to the Chapman‐Enskog expansion in kinetic theory is applied to systems of linear evolution equations. The uniform convergence of the asymptotic solution to the exact one is shown. The algorithm is applied to the linearized Carleman model of the Boltzmann equation, to the neutron transport equation, and to the Fokker‐Planck equat

ISSN:0170-4214    

DOI:10.1002/mma.1670030113

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractA method is described for constructing upper and lower bounds for the stationary values of a general class of convex functionals. The method relies of the existence of approximating convex functionals whose Gâteaux derivatives are presumed to have simpler structure than the original. The method is iterative in that convergent sequences of bounds can be constructed. Some applications to the Laplacian operator are included

ISSN:0170-4214    

DOI:10.1002/mma.1670030114

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractA one‐dimensional model for the equations of motion of a “simple fluid” according to Noll is proposed. An exterior problem for the model equation is solved by means of a transform m

ISSN:0170-4214    

DOI:10.1002/mma.1670030115

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

The Neumann and Dirichlet boundary value problem of generalized potential theory is considered. Based on a compact imbedding result, existence and uniqueness theorems are obtained for Riemannian manifolds with compact boundary (‘interior and exterior domains

ISSN:0170-4214    

DOI:10.1002/mma.1670030116

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractWe study existence and uniqueness of classical solutions of the initial value problem for Vlasov's equation with an unmodified Newtonian or Coulomb force. We give a necessary and sufficient condition for the existence of a solution on an interval I.

ISSN:0170-4214    

DOI:10.1002/mma.1670030117

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractThe treatment of certain electro‐ and magnetostatic boundary and transmission problems by boundary integral equations leads to parameter‐dependent integral equations of the second kind. The integral operators involved have the property that the dimension of their nullspaces changes between two nonzero values (depending on the geometry of the problem) as the parameter tends to zero. We investigate the continuous dependence of solutions to these equations on the parameter. To this end, we treat the problem of continuous dependence of solutions to parameter‐dependent linear operator equations of the second kind in a Banach space in the framework of generalized inv

ISSN:0170-4214    

DOI:10.1002/mma.1670030118

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractWe present three conditions for the existence of shock curves of hyperbolic 1‐conservation laws. If at least two of the conditions hold, then shock curves exist uniquely in the classical sense. We present an example (Example 2, Section 4) for which two of the conditions do not hold and a new kind of singularity occurs. In Remark 1 we present two other conditions similar to the above three conditions which also imply the existence of shock curve

ISSN:0170-4214    

DOI:10.1002/mma.1670030119

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractIn this paper we consider a string moving in its plane and subject to solid friction (Coulomb's law). It is known that when the time increases indefinitely the string reaches an equilibrium position and by analogy with the case of a mass point we ask if the equilibrium is reached after a finite time. We prove that this is the case when the string is initially at rest and 1. when the initial shape possesses a second derivative bounded by certain limits, or 2. when the initial shape is formed by two straight line segments. In the last section we obtain some partial results when the string is initially at rest in the shape of a polygonal line. The case of an arbitrary initial position is still an open problem.

ISSN:0170-4214    

DOI:10.1002/mma.1670030120

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractThis paper provides a rigorous approach to the problem of bifurcation of periodic orbits of a chemical reactor system recently studied by Marek and Stuckl, and by Neu. Using transformation techniques and invariant manifold theory the problem is reduced to a two‐parameter bifurcation equation in

ISSN:0170-4214    

DOI:10.1002/mma.1670030121

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY