摘要:

AbstractIn part 1Math. meth. in the Appl. Sci, 10, 125–144 (1988).we studied the principle of limiting absorption for local perturbations Ω of then‐dimensional domain Ω0= ℝn−1× (0, π). In this second part we extend our investigations to the time‐dependent theory and show that absence of admissible standing waves implies the validity of the principle of limiting amplitude for every frequency ω≥0 ifn≠ 3 and for ω ≠ 2, 3,… ifn= 3, respectively. In particular, the principle of limiting amplitude holds for every ω≥0 in the casen≠ 3 and for every ω ≠ 2, 3,… in the casen= 3 if Ω≠Ω0andν·x′ ⩽0 on ∂Ω, wherex′ = (x1,…,xn−1, 0) and ν is the normal unit vector on ∂Ω pointing into the complement of Ω This result stands in remarkable contrast to the fact that both principles are violated in the case of the unperturbed domain Ω0at the frequencies ω = 1, 2,… ifn⩽3. The question of the asymptotic behaviour of the solution ast→

ISSN:0170-4214    

DOI:10.1002/mma.1670110101

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractWe investigate some variational inequalities associated with the equations of the stationary motion of granulated media with a constant density. These inequalities replace the usual equations of motion in the case when some additional constraints are imposed on the flow.We prove the existence of solutions of the inequalities, study their regularity, uniqueness, dependence on data and relations to solutions of the equations of motion.

ISSN:0170-4214    

DOI:10.1002/mma.1670110102

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractIt is shown how Newton–Sabatier methods (arising in inverse scattering at fixed energy) can be related to spectral measures and typically when they correspond to regular potentials. A number of spectral formulae for various transmutation kernels are also given in terms of general Kontorovič–Lebedev theory and connections to generating functions, generalized orthogonal polynomials, etc. are indic

ISSN:0170-4214    

DOI:10.1002/mma.1670110103

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractWe consider the quasi‐linear hyperbolic initial value problem (1) of the Introduction, and prove that for anyT>0 there is a bound such that if the norm of the initial data is smaller than that bound then the solution of (1) exists on all of [0,T

ISSN:0170-4214    

DOI:10.1002/mma.1670110104

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractWe consider a three‐dimensional hyperelastic cylinder in Ω =D× [0, ∞]. We study the asymptotic behaviour of the deformations of the cross‐sections in an equilibrium state. In this case we show that the solutions either have exponential decay or exponential growth. We give some initial conditions such that the latter case

ISSN:0170-4214    

DOI:10.1002/mma.1670110105

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractDuring fertilization of certain echinoderms, a long actin‐filled tube is extended by the sperm towards the interior of the egg. This yields a parabolic free boundary problem, which differs from the classical one‐phase Stefan problem by the presence of a convective term in the partial differential equation, and because the equilibrium interface condition θ(s(t),t) = 0 is here replaced by a kinetic laws′(t) =vθ(s(t),t). This problem is set in variational form and the existence of a solution is proved by means of a Faedo–Galerkin approximation

ISSN:0170-4214    

DOI:10.1002/mma.1670110106

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractIn this paper we generalize recent theoretical results on the local continuation of parameter‐dependent non‐linear variational inequalities. The variational inequalities are rather general and describe, for example, the buckling of beams, plates or shells subject to obstacles. Under a technical hypothesis that is satisfied by the simply supported beam, we obtain the existence of a continuation of both the solution and the eigenvalue with respect to a local parameter. A numerical continuation method is presented that easily overcomes turning points. Numerical results are presented for the non‐linear

ISSN:0170-4214    

DOI:10.1002/mma.1670110107

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractError estimates are shown for some spatially discrete Galerkin finite element methods for a non‐linear heat equation. The approximation schemes studied are based on the introduction of the enthalpy as a new dependent variable, and also on the application of the Kirchhoff transformation and on interpolation of the non‐linear coefficients into standard Lagrangian finite element spa

ISSN:0170-4214    

DOI:10.1002/mma.1670110108

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractAn asymptotic expansion is derived by the multiple scales method for the electromagnetic potential in a one‐dimensional model problem for eddy current computations in periodic non‐homogeneous layered media in presence of an integral constraint for each period.Error estimates for approximations with partial sums of any order are established. Numerical computations of correctors up to the fourth order are performed and the results are compared with the exact solution in some significant ca

ISSN:0170-4214    

DOI:10.1002/mma.1670110109

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY