摘要:

AbstractA particular elastohydrodynamic lubrication problem is modelled in this work. The presence of elasticity, lubrication and cavitation calls for a non‐linear coupled system of variational equations. The existence of a solution is deduced by means of a constructive algorithm that decouples biharmonic equation of the elastic hinged plate and the lubrication‐cavitation Elrod‐Adams free boundary pr

ISSN:0170-4214    

DOI:10.1002/mma.1670180402

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA Newton method is presented for the approximate solution of the inverse problem to determine the shape of a sound‐soft or perfectly conducting arc from a knowledge of the far‐field pattern for the scattering of time‐harmonic plane waves. Fréchet differentiability with respect to the boundary is shown for the far‐field operator, which for a fixed incident wave maps the boundary arc onto the far‐field pattern of the scattered wave. For the sake of completeness, the first part of the paper gives a short outline on the corresponding direct problem via an integral equation method including the numerica

ISSN:0170-4214    

DOI:10.1002/mma.1670180403

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractWe consider the equations of motion to slightly compressible fluids and we prove that solutions converge, in thestrongnorm, to the solution of the equations of motion of incompressible fluids, as the Mach number goes to zero. From a physical point of view this means the following. Assume that we are dealing with a well‐specified fluid, so slightly compressible that we assume it to be incompressible. Our result means that the distance between the (continuous) trajectories of the real and of the idealized solution is ‘small’ with respect to the natural metric, i.e. the metric that endows the data

ISSN:0170-4214    

DOI:10.1002/mma.1670180404

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractIn this paper, we consider non‐negative solutions ofWe prove that ifpq⩽ 1 every solution remains bounded, while all solutions blow up in a finite time ifpq>1. We also show that ifp,q>1, then blow‐up can only occur on the bou

ISSN:0170-4214    

DOI:10.1002/mma.1670180405

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractLet Xbe a Banach space of real‐valued functions on [0, 1] and let ℒ(X) be the space of bounded linear operators onX. We are interested in solutionsR:(0, ∞) → ℒ(X) for the operator Riccati equation\documentclass{article}\pagestyle{empty}\begin{document}$$ R′ + TR + RT = TB_1 (t) + TB_2 (t)R + RTB_3 (t) + RTB_4 (t)R, $$\end{document}whereTis an unbounded multiplication operator inXand theBi(t)'s are bounded linear integral operators onX. This equation arises in transport theory as the result of an invariant embedding of the Boltzmann equation. Solutions which are of physical interest are those that take on values in the space of bounded linear operators onL1(0, 1). Conditions onX, R(0),T, and the coefficients are found such that the theory of non‐linear semigroups may be used to prove global existence of strong solutions in ℒ(X) that also satisfyR(t) ϵ ℒ(L1(0

ISSN:0170-4214    

DOI:10.1002/mma.1670180406

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670180401

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY