共查询到20条相似文献,搜索用时 15 毫秒
1.
A. M. Shermenev 《Journal of Mathematical Sciences》2008,152(4):608-615
Nonlinear corrections to some classical solutions of the linear diffusion equation in cylindrical coordinates are studied
within quadratic approximation. When cylindrical coordinates are used, we try to find a nonlinear correction using quadratic
polynomials of Bessel functions whose coefficients are Laurent polynomials of radius. This usual perturbation technique inevitably
leads to a series of overdetermined systems of linear algebraic equations for the unknown coefficients (in contrast with the
Cartesian coordinates). Using a computer algebra system, we show that all these overdetermined systems become compatible if
we formally add one function on radius W(r). Solutions can be constructed as linear combinations of these quadratic polynomials of the Bessel functions and the functions
W(r) and W′(r). This gives a series of solutions to the nonlinear diffusion equation; these are found with the same accuracy as the equation
is derived.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 1, pp. 235–245, 2007. 相似文献
2.
Let Aut(G) and E(G) denote the automorphism group and the edge set of a graph G, respectively. Weinberg's Theorem states that 4 is a constant sharp upper bound on the ratio |Aut(G)|/|E(G)| over planar (or spherical) 3‐connected graphs G. We have obtained various analogues of this theorem for nonspherical graphs, introducing two Weinberg‐type bounds for an arbitrary closed surface Σ, namely: where supremum is taken over the polyhedral graphs G with respect to Σ for WP(Σ) and over the graphs G triangulating Σ for WT(Σ). We have proved that Weinberg bounds are finite for any surface; in particular: WP = WT = 48 for the projective plane, and WT = 240 for the torus. We have also proved that the original Weinberg bound of 4 holds over the graphs G triangulating the projective plane with at least 8 vertices and, in general, for the graphs of sufficiently large order triangulating a fixed closed surface Σ. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 220–236, 2000 相似文献
3.
The problem of capture in a pursuit game which is described by a linear retarded functional differential equation is considered. The initial function belongs to the Sobolev space W2(1). The target is either a subset of W2(1) a point in W2(1), a subset of the Euclidean space En or a point of En. There is capture if the initial function can be forced to the target by the pursuer no matter what the quarry does. The concept of capture therefore formalizes the concepts of controllability under unpredictable disturbances. This is proved to be equivalent to the controllability of an associated linear retarded functional differential equation. There is nothing in (2) (6) or (7) below which restricts the control sets to be of the same dimension as the phase space. Our results can be applied in (2) for example, if the constraint sets Q′, P′ are subsets of Em and Ei respectively with q(t) = C(t) q′(t), − p(t) = B(t) p′(t), q′(t) ε Emp′(t) ε Er and B(t) is an n × r′-matrices and C(t) an n × m-matrix. 相似文献
4.
We consider a particular case of the nonlinear heat equation on a straight line. A family of exact solutions of the form p(t) + q(t) cos (x/
) is constructed, where p(t) and q(t) satisfy some dynamical system. A detailed analysis of the system is given. The existence of blowup solutions as well as
solutions that decay to a nonzero background is proved for the Cauchy problem for the given equation. Part of the solutions
from this family are close in a certain sense to the analytical solution of the nonlinear equation with power nonlinearities
evolving in the S-regime. Profiles of various solutions are constructed and localization is investigated numerically.
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Translated from Prikladnaya Matematika i Informatika, No. 24, pp. 5–23, 2006. 相似文献
5.
V. I. Fomin 《Differential Equations》2008,44(3):449-451
In a Banach space E, we study the equation 1 $$ u''(t) + Bu'(t) + Cu(t) = f(t), 0 \leqslant t < \infty $$ , where f(t) ∈ C([0,∞);E), B,C ∈ N(E), and N(E) is the set of closed unbounded linear operators from E to E with dense domain in E. We find a two-parameter family of solutions of Eq. (1) in two cases: (a) the operator discriminant D = B 2 ? 4C of Eq. 1 is zero; (b) D = F 2, where F is some operator in N(E). We suggest a method for increasing the smoothness of such solutions by imposing more restrictive conditions on the input data W = (B,C,f(t)) and the parameters x 1, x 2 ∈ E. 相似文献
6.
V.Yu. Slyusarchuk 《Ukrainian Mathematical Journal》2010,62(6):970-981
Let E be a finite-dimensional Banach space, let C0(R; E) be a Banach space of functions continuous and bounded on R and taking values in E; let K:C
0(R ,E) → C
0(R, E) be a c-continuous bounded mapping, let A: E → E be a linear continuous mapping, and let h ∈ C
0(R, E). We establish conditions for the existence of bounded solutions of the nonlinear equation
\fracdx(t)dt + ( Kx )(t)Ax(t) = h(t), t ? \mathbbR \frac{{dx(t)}}{{dt}} + \left( {Kx} \right)(t)Ax(t) = h(t),\quad t \in \mathbb{R} 相似文献
7.
We introduce W‐spin structures on a Riemann surface Σ and give a precise definition to the corresponding W‐spin equations for any quasi‐homogeneous polynomial W. Then we construct examples of nonzero solutions of spin equations in the presence of Ramond marked points. The main result of the paper is a compactness theorem for the moduli space of the solutions of W‐spin equations when W = W(x1, …, xt) is a nondegenerate, quasi‐homogeneous polynomial with fractional degrees (or weights) qi < ½ for all i. In particular, the compactness theorem holds for the superpotentials E6, E7, E8 or An ? 1, Dn + 1 for n ≥ 3. © 2008 Wiley Periodicals, Inc. 相似文献
8.
9.
In this paper, we consider the higher dimensional nonlinear beam equation:utt + △2u + σu + f(u)=0 with periodic boundary conditions, where the nonlinearity f(u) is a real-analytic function of the form f(u)=u3+ h.o.t near u=0 and σ is a positive constant. It is proved that for any fixed σ>0, the above equation admits a family of small-amplitude, linearly stable quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system. 相似文献
10.
M. A. Nudelman 《Integral Equations and Operator Theory》2007,58(2):273-299
Let
11.
Let F be a non-formally real field of characteristic not 2 and let W(F) be the Witt ring of F. In certain cases generators for the annihilator ideal are determined. Aim the primary decomposition of A(F) is given. For formally d fields F, as an analogue the primary decomposition of At(F) = {f(X) ∈ Z[X]| f(ω) = 0 for all ω ∈ Wt(F)}, where Wt(F) is the torsion part of the Witt group, is obtained. 相似文献
12.
Idempotent Modules in the Stable Category 总被引:3,自引:0,他引:3
Let G be a finite group and k be an algebraically closed fieldof prime characteristic. Corresponding to each closed homogeneoussubvariety W of the maximal ideal spectrum of H*(G, k) we construct(usually infinite-dimensional) kG-modules E(W) and F(W) whichare idempotent in the sense that E(W) and F(W) are isomorphic(up to projective summands) to E(W) E(W) and F(W) F(W) respectively.We study the properties of these modules, and as an applicationwe use them to describe natural direct sum decompositions ofmodules in quotient categories. 相似文献
13.
We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the
same equation:
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