共查询到20条相似文献,搜索用时 31 毫秒
1.
J. Douglas Wright Arnd Scheel 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(4):535-570
We consider a system of weakly coupled KdV equations developed initially by Gear & Grimshaw to model interactions between
long waves. We prove the existence of a variety of solitary wave solutions, some of which are not constrained minimizers.
We show that such solutions are always linearly unstable. Moreover, the nature of the instability may be oscillatory and as
such provides a rigorous justification for the numerically observed phenomenon of “leapfrogging.” 相似文献
2.
In this paper, we study stochastic functional differential equations (sfde's) whose solutions are constrained to live on
a smooth compact Riemannian manifold. We prove the existence and uniqueness of solutions to such sfde's. We consider examples
of geometrical sfde's and establish the smooth dependence of the solution on finite-dimensional parameters.
Received: 6 July 1999 / Revised version: 19 April 2000 /?Published online: 14 June 2001 相似文献
3.
We consider the asymptotic behaviour of positive solutions u of the conformal scalar curvature equation, , in the neighbourhood of isolated singularities in the standard Euclidean ball. Although asymptotic radial symmetry for such
solutions was proved some time ago, [2], we present a much simpler and more geometric derivation of this fact. We also discuss
a refinement, showing that any such solution is asymptotic to one of the deformed radial singular solutions. Finally we give
some applications of these refined asymptotics, first to computing the global Pohožaev invariants of solutions on the sphere
with isolated singularities, and then to the regularity of the moduli space of all such solutions.
Oblatum 26-II-1997 & 6-II-1998 / Published online: 12 November 1998 相似文献
4.
A mathematical program with a rational objective function may have irrational algebraic solutions even when the data are integral.
We suggest that for such problems the optimal solution will be represented as follows: If λ* denotes the optimal value there
will be given an intervalI and a polynomialP(λ) such thatI contains λ* and λ* is the unique root ofP(λ) inI. It is shown that with this representation the solutions to convex quadratic fractional programs and ratio games can be obtained
in polynomial time. 相似文献
5.
S. Yu. Vernov 《Theoretical and Mathematical Physics》2008,155(1):544-556
We construct a dark energy model with a phantom scalar field, a standard scalar field, and a polynomial potential inspired
by string field theory. We find a two-parameter set of exact solutions of the Friedmann equations. We find a potential satisfying
the conditions obtained from the string theory and such that at large times, some of the exact solutions correspond to the
state parameter wDE > −1 while the others correspond to wDE < −1. We demonstrate that the superpotential method is very effective for seeking new exact solutions.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 47–61, April, 2008. 相似文献
6.
Andrzej Rozkosz 《Probability Theory and Related Fields》2003,125(3):393-407
We extend the definition of solutions of backward stochastic differential equations to the case where the driving process
is a diffusion corresponding to symmetric uniformly elliptic divergence form operator. We show existence and uniqueness of
solutions of such equations under natural assumptions on the data and show its connections with solutions of semilinear parabolic
partial differential equations in Sobolev spaces.
Received: 22 January 2002 / Revised version: 10 September 2002 / Published online: 19 December 2002
Research supported by KBN Grant 0253 P03 2000 19.
Mathematics Subject Classification (2002): Primary 60H30; Secondary 35K55
Key words or phrases: Backward stochastic differential equation – Semilinear partial differential equation – Divergence form operator – Weak solution 相似文献
7.
Pierpaolo Soravia 《Applied Mathematics and Optimization》2009,59(2):175-201
When Hamiltonians are nonsmooth, we define viscosity solutions of the Aronsson equation and prove that value functions of
the corresponding deterministic optimal control problems are solutions if they are bilateral viscosity solutions of the Hamilton-Jacobi-Bellman
equation. We characterize such a property in several ways, in particular it follows that a value function which is an absolute
minimizer is a bilateral viscosity solution of the HJB equation and these two properties are often equivalent. We also determine
that bilateral solutions of HJB equations are unique among absolute minimizers with prescribed boundary conditions.
This research was partially supported by MIUR-Prin project “Metodi di viscosità, metrici e di teoria del controllo in equazioni
alle derivate parziali nonlineari”. 相似文献
8.
We study the global analytic properties of the solutions of a particular family of Painlevé VI equations with the parameters
β=γ=0, δ= and 2α=(2μ-1)2 with arbitrary μ, 2μ≠∈ℤ. We introduce a class of solutions having critical behaviour of algebraic type, and completely compute
the structure of the analytic continuation of these solutions in terms of an auxiliary reflection group in the three dimensional
space. The analytic continuation is given in terms of an action of the braid group on the triples of generators of the reflection
group. We show that the finite orbits of this action correspond to the algebraic solutions of our Painlevé VI equation and
use this result to classify all of them. We prove that the algebraic solutions of our Painlevé VI equation are in one-to-one
correspondence with the regular polyhedra or star-polyhedra in the three dimensional space.
Oblatum 19-III-1999 & 25-XI-1999?Published online: 21 February 2000 相似文献
9.
A. V. Domrin 《Theoretical and Mathematical Physics》2008,154(2):184-200
By Uhlenbeck’s results, every harmonic map from the Riemann sphere S2 to the unitary group U(n) decomposes into a product of so-called unitons: special maps from S2 to the Grassmannians Gr
k(ℂn) ⊂ U(n) satisfying certain systems of first-order differential equations. We construct a noncommutative analogue of this
factorization, applicable to those solutions of the noncommutative unitary sigma model that are finite-dimensional perturbations
of zero-energy solutions. In particular, we prove that the energy of each such solution is an integer multiple of 8π, give examples of solutions that are not equivalent to Grassmannian solutions, and study the realization of non-Grassmannian
zero modes of the Hessian of the energy functional by directions tangent to the moduli space of solutions.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 220–239, February, 2008. 相似文献
10.
Julie Clutterbuck Oliver C. Schnürer Felix Schulze 《Calculus of Variations and Partial Differential Equations》2007,29(3):281-293
We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge
spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay
rates.
The authors are members of SFB 647/B3 “Raum – Zeit – Materie: Singularity Structure, Long-time Behaviour and Dynamics of Solutions
of Non-linear Evolution Equations”. 相似文献
11.
Stanley Alama Lia Bronsard Changfeng Gui 《Calculus of Variations and Partial Differential Equations》1997,5(4):359-390
We study entire solutions on of the elliptic system where is a multiple-well potential. We seek solutions which are “heteroclinic,” in two senses: for each fixed they connect (at ) a pair of constant global minima of , and they connect a pair of distinct one dimensional stationary wave solutions when . These solutions describe the local structure of solutions to a reaction-diffusion system near a smooth phase boundary curve.
The existence of these heteroclinic solutions demonstrates an unexpected difference between the scalar and vector valued Allen–Cahn
equations, namely that in the vectorial case the transition profiles may vary tangentially along the interface. We also consider
entire stationary solutions with a “saddle” geometry, which describe the structure of solutions near a crossing point of smooth
interfaces.
Received April 15, 1996 / Accepted: November 11, 1996 相似文献
12.
Let be the approximation exponent of a power series α (so that when α is algebraic of degree d, then by Dirichlet’s and Liouville’s Theorems). If the characteristic is positive, q is a power of the characteristic, and are related by a fractional linear transformation with polynomial coefficients, then by respective work of Voloch and of de Mathan, there are constants such that has no solution if , and infinitely many solutions if . We will formulate and prove generalizations to simultaneous approximation. 相似文献
13.
We introduce and study a new concept of a weak elliptic equation for measures on infinite dimensional spaces. This concept
allows one to consider equations whose coefficients are not globally integrable. By using a suitably extended Lyapunov function
technique, we derive a priori estimates for the solutions of such equations and prove new existence results. As an application,
we consider stochastic Burgers, reaction-diffusion, and Navier-Stokes equations and investigate the elliptic equations for
the corresponding invariant measures. Our general theorems yield a priori estimates and existence results for such elliptic
equations. We also obtain moment estimates for Gibbs distributions and prove an existence result applicable to a wide class
of models.
Received: 23 January 2000 / Revised version: 4 October 2000 / Published online: 5 June 2001 相似文献
14.
We study the structure of optimal solutions for a class of constrained, second order variational problems on bounded intervals.
We show that, for intervals of length greater than some positive constant, the optimal solutions are bounded inC
1 by a bound independent of the length of the interval. Furthermore, for sufficiently large intervals, the ‘mass’ and ‘energy’
of optimal solutions are almost uniformly distributed. 相似文献
15.
Alexey V. Kapustyan Alexey V. Pankov J. Valero 《Set-Valued and Variational Analysis》2012,20(3):445-465
In this paper we prove the existence of solutions for the 3D Bénard system in the class of functions which are strongly continuous with respect to the second component of the vector (that is, the one corresponding to the parabolic equation). We construct then a multivalued semiflow generated by such solutions and obtain the existence of a global φ −attractor for the weak-strong topology. Moreover, a family of multivalued semiflows is defined on suitable convex bounded subsets of the phase space, proving for them the existence of a global attractor (which is the same for every semiflow of the family) for the weak-strong topology. 相似文献
16.
Markos Katsoulakis Georgios T. Kossioris Fernando Reitich 《Journal of Geometric Analysis》1995,5(2):255-279
We study asharpinterface model for phase transitions which incorporates the interaction of the phase boundaries with the walls of a container Ω. In
this model, the interfaces move by their mean curvature and are normal to δΩ. We first establish local-in-time existence and
uniqueness of smooth solutions for the mean curvature equation with a normal contact angle condition. We then discuss global
solutions by interpreting the equation and the boundary condition in a weak (viscosity) sense. Finally, we investigate the
relation of the aforementioned model with atransitionlayer model. We prove that if Ω isconvex, the transition-layer solutions converge to the sharp-interface solutions as the thickness of the layer tends to zero. We
conclude with a discussion of the difficulties that arise in establishing this result in nonconvex domains.
Communicated by David Kinderlehrer 相似文献
17.
For an arbitrary domain Ω ⊂ ℝn, n=2,3, Ω ≠ ℝn, we prove the existence of weak periodic solutions to the Navier-Stokes equations and of regular solutions if the data are
small or satisfy certain symmetry conditions. We also show that the periodic regular solutions are stable. Bibliography: 38
titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 233, 1996, pp. 142–182. 相似文献
18.
We consider the existence and uniqueness of singular solutions for equations of the formu
1=div(|Du|p−2
Du)-φu), with initial datau(x, 0)=0 forx⇑0. The function ϕ is a nondecreasing real function such that ϕ(0)=0 andp>2.
Under a growth condition on ϕ(u) asu→∞, (H1), we prove that for everyc>0 there exists a singular solution such thatu(x, t)→cδ(x) ast→0. This solution is unique and is called a fundamental solution. Under additional conditions, (H2) and (H3), we show the
existence of very singular solutions, i.e. singular solutions such that ∫|x|≤r
u(x,t)dx→∞ ast→0. Finally, for functions ϕ which behave like a power for largeu we prove that the very singular solution is unique. This is our main result.
In the case ϕ(u)=u
q, 1≤q, there are fundamental solutions forq<p*=p-1+(p/N) and very singular solutions forp-1<q<p*. These ranges are optimal.
Dedicated to Professor Shmuel Agmon 相似文献
19.
Adrien Blanchet José A. Carrillo Philippe Laurençot 《Calculus of Variations and Partial Differential Equations》2009,35(2):133-168
This paper is devoted to the analysis of non-negative solutions for a generalisation of the classical parabolic-elliptic Patlak–Keller–Segel
system with d ≥ 3 and porous medium-like non-linear diffusion. Here, the non-linear diffusion is chosen in such a way that its scaling
and the one of the Poisson term coincide. We exhibit that the qualitative behaviour of solutions is decided by the initial
mass of the system. Actually, there is a sharp critical mass M
c
such that if solutions exist globally in time, whereas there are blowing-up solutions otherwise. We also show the existence of self-similar
solutions for . While characterising the possible infinite time blowing-up profile for M = M
c
, we observe that the long time asymptotics are much more complicated than in the classical Patlak–Keller–Segel system in
dimension two.
This paper is under the Creative Commons licence Attribution-NonCommercial-ShareAlike 2.5. 相似文献
20.
A. V. Domrin 《Theoretical and Mathematical Physics》2008,156(3):1231-1246
Using a noncommutative version of the uniton theory, we study the space of those solutions of the noncommutative U(1) sigma
model that are representable as finite-dimensional perturbations of the identity operator. The basic integer-valued characteristics
of such solutions are their normalized energy e, canonical rank r, and minimum uniton number u, which always satisfy r ≤ e
and u ≤ e. Starting with the so-called BPS solutions (u = 1), we completely describe the sets of all solutions with r = 1,
2, e − 1, e (which forces u ≤ 2) and all solutions of small energy (e ≤ 5). The obtained results reveal a simple but nontrivial
structure of the moduli spaces and lead to a series of conjectures.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 307–327, September, 2008. 相似文献