摘要:

We examine the possibility that thermal runaway may occur locally in the earth's asthenosphere, due to a coupling between the velocity and temperature fields due to a strongly temperature‐dependent viscosity. The analysis is based on a partial description of convection in the earth, in which the boundary‐layer nature of the motion is taken into account. We find that realistic parameter values are consistent with thermal runaway occurring on length scales of thousands of kilometers, or time scales of order 108years. If thermal runaway does occur, one would expect partial melting, and probably consequent volcan

ISSN:0022-2526    

DOI:10.1002/sapm19867411

年代:1986

数据来源: WILEY

摘要:

The stability of steady‐state solutions of reaction‐advection‐diffusion equations to perturbations in the initial data is examined by means of a comparison theorem. In particular, conditions on the reactive terms and the advective terms are used to prove stability or asymptotic stability of steady boundary‐layer and shock‐layer solutions and to estimate the maximum allowable size of the initial perturbation. Many examples are discussed, including the time‐dependent Lagerstrom‐Cole problem and a problem modeling transonic flow in a no

ISSN:0022-2526    

DOI:10.1002/sapm198674135

年代:1986

数据来源: WILEY

摘要:

We consider evolution equations, mainly of typeut= F(u, ux,..., ∂ku/∂xk), which describe pseudo‐spherical surfaces. We obtain a systematic procedure to determine a linear problem for which a given equation is the integrability condition. Moreover, we investigate how the geometrical properties of surfaces provide analytic information for such equa

ISSN:0022-2526    

DOI:10.1002/sapm198674155

年代:1986

数据来源: WILEY

摘要:

A simple analytical model has been constructed to demonstrate Saffman's (1985) proof of Tanaka's (1983, 1985) results on the superharmonic stability of deep water waves. The model shows the change of geometrical and algebraic multiplicity of the eigenvalues and eigenvectors of the stability equation at the critical points. It confirms the existence of Hamiltonian systems with limit points at which there is no change of stability.

ISSN:0022-2526    

DOI:10.1002/sapm198674185

年代:1986

数据来源: WILEY