摘要:

AbstractIn this paper we prove the existence and uniqueness of solutions of the leakage problem for the Euler equations in bounded domain Ω C R3with corners π/n, n= 2, 3… We consider the case where the tangent components of the vorticity vector are given on the partS1of the boundary where the fluid enters the domain. We prove the existence of an unique solution in the Sobolev spaceWpl(Ω), for arbitrary naturallandp>1. The proof is divided on three parts: (1) the existence of solutions of the elliptic problem in the domain with corners\documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm rot }\upsilon {\rm = }\omega {\rm, div }\upsilon = 0,\upsilon \cdot \bar n||_{\partial \Omega } = 6 $$\end{document}wherev– velocity vector, ω – vorticity vector andnis an unit outward vector normal to the boundary, (2) the existence of solutions of the following evolution problem for given velocity vector\documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{l} \omega _t + \upsilon ^\kappa \omega _x \kappa - \omega ^\kappa \upsilon _x \kappa = F \equiv {\rm rot }f \\ \omega |_{t = 0} = \omega _0,\omega |_{s1} = \eta \\ \end{array} $$\end{document}(3) the method of successive approximations, using solvability of problems (1

ISSN:0170-4214    

DOI:10.1002/mma.1670040102

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractIn the paper we prove the existence and uniqueness of solutions of the overdetermined elliptic system\documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {\left( {\rm A} \right)} & {{\rm rot }\upsilon {\rm = }\omega } & {{\rm div }\upsilon {\rm = 0}} & {\upsilon \cdot {\rm }\bar n|_{\partial \Omega } = b} \\ \end{array} $$\end{document}whereb, ω are given functions, in a domain ΩCR3with corners π/n, n= 2, 3, … The proof is divided on two steps, we construct a solution for the Laplace equation in a dihedral angle π/n, using the method of reflection and we get an estimate in the norms of the Sobolev spaces in some neighbourhood of the edge. In the dihedral angle system (A) reduces to the Dirichlet and Neumann problems for the Laplace equation. In the next step we prove the existence of solutions in the Sobolev spacesWpl(Ω) using the existence of generalized solutions

ISSN:0170-4214    

DOI:10.1002/mma.1670040103

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThe theory of part I is applied to prove several existence and non‐existence results for special cases. IfN= 3, a global classical solution ofP° exists, if φ ⩾ 0 has rotational symmetry. IfN⩾ 4, global classical solutions ofP° do not alwa

ISSN:0170-4214    

DOI:10.1002/mma.1670040104

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractOne considers an elastic halfspace with depth (x1) dependent density Q and Lamé moduli (λ,m̈). Impulsive stresses τli= δ(x2,x3)δ(t) forx1= 0 are applied with displacement responsesui=gi(t,x2,x3) atx1= 0 (i= 1, 2, 3). Letvi(t,x1) = ∫∫uidx2dx3(i= 1, 2 is enough) and setw(t,x1) = ∫∫x2u1dx2dx3. One obtains a system of 3 differential equations forv1,v2, andwto which the spectral techniques of inverse scattering theory are applied as in [25]. The inverse problems for the uncoupledvican then be solved to produce 2 functionsA1andA2involving (Q, λ, μ) as functions of “bound” variablesy1andy2containing (Q, λ, μ), between which a relation then is determined. Analysis of the coupled equation forwthen leads to a Fredholm integral equation whose solution provides an additional relation between (Q, λ, μ) from which (Q, λ, μ) can be determined as functions ofx1. The integral equation is reduced to a Volterra type equation by results and techniques of transmutation and then solved by a modification of standard techniques. A number of features and results of independent mathematical interest arise from

ISSN:0170-4214    

DOI:10.1002/mma.1670040105

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractA study and the solution of an extension of the classical Sommerfeld half‐plane problem which leads to a pair of integral equations of the Wiener‐Hopf type is given. The method of solution is function theoretic in character and employs a combination of the ideas of Wiener and Hopf and Carle

ISSN:0170-4214    

DOI:10.1002/mma.1670040106

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThe ‘anti‐dynamo’ theorems for poloidal magnetic fields with axisymmetry and plane symmetry are generalized to the case of a compressible and time‐dependent flow in a fluid with arbitrary condu

ISSN:0170-4214    

DOI:10.1002/mma.1670040107

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThe aim of this work is to give theoretical justification of several types of finite element approximations to the initial‐boundary value problems of first order linear hyperbolic equations. Our approximate scheme is obtained by the piecewise linear continuous finite element method for space variable,x, and the Euler type step by step integration method for time variable,t. An artificial viscosity technique, up‐stream type methods are considered within the frame work ofL2‐theory. The convergence and the error estimate of the approximate solutions to the true one are disc

ISSN:0170-4214    

DOI:10.1002/mma.1670040108

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThe Maxwell equations are formulated as an evolution equation in a suitable chosen Hilbert space involving a densely defined closed skew‐Hermitian operator which generates a unitary group. A Crank‐Nicolsen‐Galerkin approximation is then established and convergence is shown by arguments from the theory of approximation of groups of oper

ISSN:0170-4214    

DOI:10.1002/mma.1670040109

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractWe study the problem\documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} { - \Delta u = \lambda H({\rm u - 1)}} & {{\rm in }\Omega } \\ {u = g} & {{\rm in }\partial \Omega } \\ \end{array} $$\end{document}(His the Heaviside unit step function) in spherical domains Ω of arbitrary dimension. Wheng= 0, there are two branches of radial solutions; for small nonzerogthere are solutions near the corresponding radial solution. Moreover, the set where μ = 1 is in all cases an analytic hypersurfac

ISSN:0170-4214    

DOI:10.1002/mma.1670040110

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractBy using the method of averaging, we give a complete Hopf bifurcation diagram when the differential equation has more than one parameter. The method is applied to a system of parabolic equations with nonlinear coupling on the boundary. This set of equations is a mathematical model which describes the normalized concentrations of substances in a solution produced by two enzymes.

ISSN:0170-4214    

DOI:10.1002/mma.1670040111

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY