ISSN:0170-4214    

DOI:10.1002/mma.1670010402

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe three‐dimensional fluid flow of a steady or unsteady moving incompressible continuous medium is considered. Several Crocco‐type transformations are applied which reduce the system of three equations of the Prandtl boundary layer to a system of two strongly coupled parabolic equati

ISSN:0170-4214    

DOI:10.1002/mma.1670010403

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractA bifurcation analysis is given for the generalized Bénard problem near the critical value of the Grashoff number. In contrast to earlier investigations where symmetry arguments were used to reduce the boundary‐value‐problem to a simple‐eigenvalue‐bifurcation, we only require double periodicity and treat high multiplicity bifurcation. It is shown that solutions of a yet unknown ty

ISSN:0170-4214    

DOI:10.1002/mma.1670010404

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractFor any differential operatorL, separable in some coordinate system, we construct a set of commuting operatorsSisuch that 1) eachSimaps solutions ofLu= 0 into solutions, and 2) the separated solutions ofLu= 0 are simultaneous eigenfunctions ofSi. Moreover, a certain description of the separable coordinate system bySiis possible. The paper generalizes results obtained by W. Miller and others on many equations of mathematical physics.

ISSN:0170-4214    

DOI:10.1002/mma.1670010405

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractFor the one‐dimensional Nernst‐Planck equations of the theory of ion‐transport in thin layers or membranes which mathematically represent a nonlinear coupled parabolic integro‐differential system some global existence and uniqueness theorems for inner and outer problems are given using a priori estimates of the maximum princip

ISSN:0170-4214    

DOI:10.1002/mma.1670010406

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe secondary wave motion in the free Ekman layer, on which a constant shear stress acts, is examined by an analytic method. The results show, that the waves move away from the center of rotation.

ISSN:0170-4214    

DOI:10.1002/mma.1670010407

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractWe consider a family of semilinear evolution equations in Hilbert space of the formwith, in general, unbounded operators *A(λ),F(λ·) depending analytically on a real parameter λ. We assume that the origin is a stationary solution, i.e.F(λ,0) = 0, for all λ εRand that the linearization (with respect tou) at the origin is given by du/dt +A(λ)u= 0. Our essential assumption is the following: A(λ) possesses one pair of simple complex conjugate eigenvalues μ(λ) = Re μ(λ) ± i Im μ(λ) such that Im μ(0)>0 andfor somemεNorIfm= 1 the curves of eigenvalues μ(λ) cross the imaginary axis transversally at ±i Im μ(0). In this case a unique branch of periodic solutions emanates from the origin at λ = 0 which is commonly called Hopf bifurcation. If μ(λ) and the imaginary axis are no longer transversal, i.e.m>1, we call a bifurcation of periodic solutions, if it occurs, a generalized Hopf bifurcation. It is remarkable that up tomsuch branches may exist. Our approach gives the number of bifurcating solutions, their direction of bifurcation, and its asymptotic expansion. We regain the results of D. Flockerzi who established them in a completely different way for ordinar

ISSN:0170-4214    

DOI:10.1002/mma.1670010408

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractWe describe an iteration procedure in a Banach space which is quadratically convergent like Newton's method. In fact, it is a modification of the latter. The inverted derivatives are replaced by so‐called contractors which are constructed recursively. Moreover, this method is extended to a scale of Banach spaces. It turns out that the rate of convergence remains quadratic, even if the norms of the contractors are increasing exponentially. A hard implicit function theorem results. In particular, this theorem can be applied to prove existence of quasiperiodic solutions for the Lorenz model of stationary convectio

ISSN:0170-4214    

DOI:10.1002/mma.1670010409

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe initial value problem for the modified Vlasov equation with a mollification parameter δ>0, as introduced by Batt, has a unique global solution in the weak sense wheneverf0εL1andf0≧ 0 λ‐a.e. Assuming boundedness off0and boundedness of the kinetic energy, it is shown that, as δ → 0, there are subsequences δn→ 0 such that the corresponding solutions converge weakly in the measure‐theoretical sense. The limits are shown to be global weak solutions of the initial value problem for Vlasov's equation, and these solutions are seen to be weakly continuous with respect tot.For the plasma physical case, boundedness of the kinetic energy is a consequence of energ

ISSN:0170-4214    

DOI:10.1002/mma.1670010410

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractWe look for solutions of systems of nonlinear elliptic equations with nonlinear boundary conditions and values in some compact convex setM.If the nonlinear terms satisfy a sign condition on the boundary ofMand the inhomogeneous terms assume their values in this set existence of solutions is proved.The proof is based on the homotopy invariance of the Leray‐Schauder degree and Weinberger's strong maximum principl

ISSN:0170-4214    

DOI:10.1002/mma.1670010411

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY