共查询到20条相似文献，搜索用时 31 毫秒
1.
We consider the stationary flow of a generalized Newtonian fluid which is modelled by an anisotropic dissipative potential f. More precisely, we are looking for a solution
of the following system of nonlinear partial differential equations
Here
denotes the pressure, g is a system of volume forces, and the tensor T is the gradient of the potential f. Our main hypothesis imposed on f is the existence of exponents 1 < p q0 < such that
holds with constants , > 0. Under natural assumptions on p and q0 we prove the existence of a weak solution u to the problem (*), moreover we prove interior C1,-regularity of u in the two-dimensional case. If n = 3, then interior partial regularity is established. 相似文献
2.
In this paper we analyze the structure of positive radial solutions for the following semi-linear equations:
|
Du + f(u,|x|)=0 \Delta u + f(u,|{\bf x}|)=0 相似文献
3.
We investigate the dynamics of the semiflow φ induced on H01(Ω) by the Cauchy problem of the semilinear parabolic equation
on Ω. Here
is a bounded smooth domain, and
has subcritical growth in u and satisfies
. In particular we are interested in the case when f is definite superlinear in u. The set
of attraction of 0 contains a decreasing family of invariant sets
distinguished by the rate of convergence
. We prove that the Wk’s are global submanifolds of
, and we find equilibria in the boundaries
. We also obtain results on nodal and comparison properties of these equilibria. In addition the paper contains a detailed exposition of the semigroup approach for semilinear equations, improving earlier results on stable manifolds and asymptotic behavior near an equilibrium.Supported by DFG Grant BA 1009/15-1. 相似文献
4.
Under certain assumptions on f and g we prove that positive, global and bounded solutions u of the non-autonomous heat equation
in
( N ≥ 3) converge to a steady state.
Dedicated to Prof. Pavol Brunovsky on the occasion of his 70th birthday. 相似文献
5.
In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles.
We find a fractional Lagrangian L( x( t), where
a
c
D
t
α
x( t)) and 0< α<1, such that the following is the corresponding Euler–Lagrange
At last, exact solutions for some Euler–Lagrange equations are presented. In particular, we consider the following equations
where g( t) and f( t) are suitable functions.
D. Baleanu is on leave of absence from Institute of Space Sciences, P.O. BOX MG-23, 76900 Magurele-Bucharest, Romania. e-mail:
baleanu@venus.nipne.ro. 相似文献
6.
We establish unimprovable (in a certain sense) sufficient conditions for the solvability and unique solvability of the boundary-value problem where
is a continuous operator satisfying the Carathéodory conditions, h: C([ a, b]; R) R is a continuous functional, and R
+. 相似文献
7.
We prove the existence of positive radial solutions of the following equation:
and give sufficient conditions on the positive functions K1( r) and K2 ( r) for the existence and nonexistence of ground states (G.S.) and Singular ground states (S.G.S.), when
or
. We also give sufficient conditions for the existence of radial S.G.S. and G.S. of equation
when
and
, respectively. We are also able to classify all the S.G.S. of this equation. The proofs use a new Emden–Fowler transform which allow us to use techniques taken from dynamical system theory, in particular the ones developed in Johnson et al. ( Nonlinear Anal, T.M.A. 20, 1279–1302 (1993)) for the problems obtained by substituting the ordinary Laplacian Δ for the m-Laplacian Δ m in the preceding equations.MSC: 37B55, 35H30, 35J70 相似文献
8.
In this paper it is shown that if p( x, u,·) is a quasiconvex function with linear growth, then the relaxed functional in BV(, p) of |
相似文献
9.
The divergence identity for punctured domain B1(0)\ {0}
suggest a viewpoint on describing the behavior of a function uC2( B1(0)\{0}) near the origin. This is useful especially on describing the singular behavior of solutions of polyharmonic equations. In this paper we mainly show that the solution u of the equation
satisfies the identity that, letting
vi=(–) iu
provided there exist s0>0 and t0 0 such that f( x, t) c| x| –tq for 0<| x|< s0 and t t0 with n– q( n–2 p) and q>1.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday. 相似文献
10.
This paper considers the second-order differential difference equation with the constant delay > 0 and the piecewise constant function
with Differential equations of this type occur in control systems, e.g., in heating systems and the pupil light reflex, if the controlling function is determined by a constant delay > 0 and the switch recognizes only the positions on [ f(>) = a] and off [ f(>) = b], depending on a constant threshold value . By the nonsmooth nonlinearity the differential equation allows detailed analysis. It turns out that there is a rich solution structure. For a fixed set of parameters a, b, , , infinitely many different periodic orbits of different minimal periods exist. There may be coexistence of three asymptotically stable periodic orbits (multistability of limit cycles). Stability or instability of orbits can be proven. 相似文献
11.
This paper examines the asymptotic behavior of measure valued solutions to the initial value problem for the nonlinear heat conduction equation |
相似文献
12.
We study the stationary Dirac equation
where M( x) is a matrix potential describing the external field, and R( x, u) stands for an asymptotically quadratic nonlinearity modeling various types of interaction without any periodicity assumption.
For ħ fixed our discussion includes the Coulomb potential as a special case, and for the semiclassical situation ( ħ → 0), we handle the scalar fields. We obtain existence and multiplicity results of stationary solutions via critical point
theory. 相似文献
13.
This paper deals with connected branches of nonstationary periodic trajectories of Hamilton equations
emanating from the degenerate stationary point
for H being the generalized Hénon-Heiles (HH) Hamiltonian:
or the generalized Yang-Mills (YM) Hamiltonian:
The existence of such branches has been proved. Minimal periods of searched trajectories near x0 have been described. 相似文献
14.
Bifurcation phenomena from standing pulse solutions of the problem
is considered. (>0) is a sufficiently small parameter and is a positive one. It is shown that there exist two types of destabilization of standing pulse solutions when decreases. One is the appearance of travelling pulse solutions via the static bifurcation and the other is that of in-phase breathers via the Hopf bifurcation. Furthermore which type of destabilization occurs first with decreasing is discussed for the piecewise linear nonlinearities f and g. 相似文献
15.
The paper is concerned with the asymptotic behavior as t of solutions u(x,t) of the equation
in the case f(0)= f(1)=0, with f(u) non-positive for u(>0) sufficiently close to zero and f(u) non-negative for u(<1) sufficiently close to 1. This guarantees the uniqueness (but not the existence) of a travelling front solution u;U(x–ct), U(–);0, U();, and it is shown in essence that solutions with monotonic initial data converge to a translate of this travelling front, if it exists, and to a stacked combination of travelling fronts if it does not. The approach is to use the monotonicity to take u and t as independent variables and p = u
x as the dependent variable, and to apply ideas of sub- and super-solutions to the diffusion equation for p.This research was sponsored by the United States Army under Contract No. DAAG29-75-C-0024. 相似文献
17.
We prove the following statement:
Theorem 1.
Let
E and
be an arbitrary infinite-dimensional Banach space and a continuous mapping, respectively. Then, for every
and > 0, there exists a continuous mapping
such that and the Cauchy problem does not have a solution for every > 0. 相似文献
18.
We consider the Cauchy problem for a strictly hyperbolic, N × N quasilinear system in one-space dimension
where , is a smooth matrix-valued map and the initial data is assumed to have small total variation. We present a front tracking algorithm that generates piecewise constant approximate
solutions converging in to the vanishing viscosity solution of (1), which, by the results in [6], is the unique limit of solutions to the (artificial)
viscous parabolic approximation as . In the conservative case where A( u) is the Jacobian matrix of some flux function F( u) with values in , the limit of front tracking approximations provides a weak solution of the system of conservation laws u
t
+ F( u)
x
= 0, satisfying the Liu admissibility conditions.
These results are achieved under the only assumption of strict hyperbolicity of the matrices A( u), . In particular, our construction applies to general, strictly hyperbolic systems of conservation laws with characteristic
fields that do not satisfy the standard conditions of genuine nonlinearity or of linear degeneracy in the sense of Lax[17], or in the generalized sense of Liu[23].
Dedicated to Prof. Tai Ping Liu on the occasion of his 60
th
birthday 相似文献
19.
We establish unimprovable sufficient conditions for the unique solvability of the boundary-value problem and for the nonnegativity of its solution; here, : C([ a, b]; R) L([ a, b]; R) is a linear bounded operator, q L([ a, b]; R), R
+, and c R. 相似文献
20.
A criterion to predict bifurcation of homoclinic orbits instrongly nonlinear self-excited one-degree-of-freedom oscillator is presented. TheLindstedt–Poincaré perturbation method is combined formally withthe Jacobian elliptic functions to determine an approximation of thelimit cycles near homoclinicity. We then apply a criterion forpredicting homoclinic orbits, based on the collision of the bifurcatinglimit cycle with the saddle equilibrium. In particular we show that thiscriterion leads to the same results, formally and to leading order, asthe standard Melnikov technique. Explicit applications of this criterionto quadratic or cubic nonlinearities f( x) are included. 相似文献
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