摘要:

AbstractOur recent paper about some new fundamental solutions is complemented by a representation of the fundamental solution of certain evolution operators of fourth order in terms of a family of fundamental solutions of operators of second order. By applying this to the operators of vibrating beams and plates we deduce representations of their fundamental solutions as simple definite integrals over tabulated functions.

ISSN:0170-4214    

DOI:10.1002/mma.1670150802

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe non‐characteristic Cauchy problem for the heat equationuxx(x,t) =u1(x,t), 0 ⩽x⩽ 1, − ∞

ISSN:0170-4214    

DOI:10.1002/mma.1670150803

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractIn this paper a necessary and sufficient condition for a pair of vector functions to be radiation patterns is presented. More precisely, it is proved that two vector functions, the first in the radial direction and the second in the tangential one, are radiation patterns if and only if there are two entire harmonic vector functions whose radial and tangential projections, respectively, are identical with the previous functions on the unit sphere and whoseL2‐norm over a sphere of radiusRis a function of exponential type in the variable

ISSN:0170-4214    

DOI:10.1002/mma.1670150804

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractLetD⊂ ℝnbe a bounded domain with piecewise‐smooth boundary, andq(x,t) a smooth function onD× [0,T]. Consider the time‐like Cauchy problemGiveng,hfor which the equation has a solution, we show how to approximateu(x,t) by solving a well posed fourth‐order elliptic partial differential equation (PDE). We use the method of quasi‐reversibility to construct the approximating PDE. We derive error estimates and present numer

ISSN:0170-4214    

DOI:10.1002/mma.1670150805

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper is concerned with non‐linear parabolic problems. This particular type of probiem arose from the study of the instability of transverse detonation waves in channels. A fairly complete account of the equilibrium states is given. A global approach is adopted for the upper and lower solutions and the energy estimates. Finally, the invariant manifolds that describe the asymptotic behaviour of the solutions near the equilibrium states are discusse

ISSN:0170-4214    

DOI:10.1002/mma.1670150806

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA useful relationship between solutions is derived for a class of matrix equations arising in the system theory, particularly in the context of the orthogonal approximation of linear dynamic systems. The computational aspects of the result are discussed and illustrated on an example of practical importance.

ISSN:0170-4214    

DOI:10.1002/mma.1670150807

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670150801

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY