共查询到20条相似文献,搜索用时 0 毫秒
1.
In the present paper, we study the Cauchy problem for a nonlinear time-dependent kinetic neutrino transport equation. We prove
the existence and uniqueness theorem for the solution of the Cauchy problem, establish uniform bounds int for the solution of this problem, and prove the existence and uniqueness of a stationary trajectory and the stabilization
ast→∞ of the solution of the time-dependent problem for arbitrary initial data.
Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 677–686, May, 1997.
Translated by A. M. Chebotarev 相似文献
2.
This current paper is devoted to the Cauchy problem for higher order dispersive equation u_t+ ?_x~(2n+1)u = ?_x(u?_x~nu) + ?_x~(n-1)(u_x~2), n ≥ 2, n ∈ N~+.By using Besov-type spaces, we prove that the associated problem is locally well-posed in H~(-n/2+3/4,-1/(2n))(R). The new ingredient is that we establish some new dyadic bilinear estimates. When n is even, we also prove that the associated equation is ill-posed in H~(s,a)(R) with s -n/2+3/4 and all a∈R. 相似文献
3.
S. Kharibegashvili B. Midodashvili 《Journal of Mathematical Analysis and Applications》2011,376(2):750-759
The Cauchy characteristic problem in the light cone of the future for one class of nonlinear hyperbolic systems of the second order is considered. The existence and uniqueness of global solution of this problem is proved. 相似文献
4.
YANG JINSHUN 《高校应用数学学报(英文版)》1995,10(2):155-166
ONTHECAUCHYPROBLEMOFNONLINEARDEGENERATEPARABOLICEQUATION¥YANGJINSHUNAbstract:Inthispaper,weprovetheexistenceofsolutionoftheCa... 相似文献
5.
Didier Pilod 《Journal of Differential Equations》2008,245(8):2055-2077
We study the higher-order nonlinear dispersive equation
6.
7.
In this work we prove that the initial value problem of the Benney-Lin equation ut + uxxx + β(uxx + u xxxx) + ηuxxxxx + uux = 0 (x ∈ R, t ≥0 0), where β 〉 0 and η∈R, is locally well-posed in Sobolev spaces HS(R) for s ≥ -7/5. The method we use to prove this result is the bilinear estimate method initiated by Bourgain. 相似文献
8.
9.
Erik Wahlén 《Journal of Mathematical Analysis and Applications》2006,323(2):1318-1324
Using a variational approach we prove an optimal nonlinear convolution inequality. This result is then applied to give criteria for finite-time blow-up of solutions to a nonlinear model equation in elasticity, improving considerably upon recent blow-up results. 相似文献
10.
We study the local solvability of the Cauchy-Dirichlet problem for the system
which describes the dynamics of an incompressible viscoelastic Kelvin-Voigt fluid. The configuration space of the problem
is described.
Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 442–450, March, 1998. 相似文献
11.
Martin Hadac 《Transactions of the American Mathematical Society》2008,360(12):6555-6572
We show the local in time well-posedness of the Cauchy problem for the Kadomtsev-Petviashvili II equation for initial data in the non-isotropic Sobolev space with and . On the scale this result includes the full subcritical range without any additional low frequency assumption on the initial data. More generally, we prove the local in time well-posedness of the Cauchy problem for the following generalisation of the KP II equation: for , , and . We deduce global well-posedness for , and real valued initial data.
12.
Yang Zhijian 《Journal of Mathematical Analysis and Applications》2006,313(1):197-217
The paper studies the existence, both locally and globally in time, stability, decay estimates and blowup of solutions to the Cauchy problem for a class of nonlinear dispersive wave equations arising in elasto-plastic flow. Under the assumption that the nonlinear term of the equations is of polynomial growth order, say α, it proves that when α>1, the Cauchy problem admits a unique local solution, which is stable and can be continued to a global solution under rather mild conditions; when α?5 and the initial data is small enough, the Cauchy problem admits a unique global solution and its norm in L1,p(R) decays at the rate for 2<p?10. And if the initial energy is negative, then under a suitable condition on the nonlinear term, the local solutions of the Cauchy problem blow up in finite time. 相似文献
13.
14.
Zhi Qian Chu-Li Fu Zhen-Ping Li 《Journal of Mathematical Analysis and Applications》2008,338(1):479-489
A Cauchy problem for the Laplace equation in a rectangle is considered. Cauchy data are given for y=0, and boundary data are for x=0 and x=π. The solution for 0<y?1 is sought. We propose two different regularization methods on the ill-posed problem based on separation of variables. Both methods are applied to formulate regularized solutions which are stably convergent to the exact one with explicit error estimates. 相似文献
15.
S. Kharibegashvili 《Journal of Mathematical Analysis and Applications》2008,338(1):71-81
We consider one multidimensional version of the Cauchy characteristic problem in the light cone of the future for a hyperbolic equation with power nonlinearity with iterated wave operator in the principal part. Depending on the exponent of nonlinearity and spatial dimension of equation, we investigate the problem on the nonexistence of global solutions of the Cauchy characteristic problem. The question on the local solvability of that problem is also considered. 相似文献
16.
B. D. Gelman 《Functional Analysis and Its Applications》2008,42(3):227-229
This note deals with an application of the fixed point theorem for multivalued contraction mappings to the study of degenerate differential equations with Lipschitz right-hand side and with degeneration determined by a closed surjective linear operator. 相似文献
17.
The paper studies the existence and nonexistence of global solutions to the Cauchy problem for a nonlinear beam equation arising in the model in variational form for the neo–Hookean elastomer rod where k1, k2>0 are real numbers, g(s) is a given nonlinear function. When g(s)=sn (where n?2 is an integer), by using the Fourier transform method we prove that for any T>0, the Cauchy problem admits a unique global smooth solution u∈C∞((0, T]; H∞( R ))∩C([0, T]; H3( R ))∩C1([0, T]; H?1( R )) as long as initial data u0∈W4, 1( R )∩H3( R ), u1∈L1( R )∩H?1( R ). Moreover, when (u0, u1)∈H2( R ) × L2( R ), g∈C2( R ) satisfy certain conditions, the Cauchy problem has no global solution in space C([0, T]; H2( R ))∩C1([0, T]; L2( R ))∩H1(0, T; H2( R )). Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
18.
Yong Zhou 《Calculus of Variations and Partial Differential Equations》2006,25(1):63-77
In this paper, firstly we find the best constant for a convolution problem on the unit circle via a variational method. Then
we apply the best constant on a nonlinear rod equation to give sufficient conditions on the initial data, which guarantee
finite time singularity formation for the corresponding solutions.
Mathematics Subject Classification (2000) 30C70, 37L05, 35Q58, 58E35 相似文献
19.
In this paper we prove that the Cauchy problem associated with the generalized KdV-BO equation ut + uxxx + λH(uxx) + u^2ux = 0, x ∈ R, t ≥ 0 is locally wellposed in Hr^s(R) for 4/3 〈r≤2, b〉1/r and s≥s(r)= 1/2- 1/2r. In particular, for r = 2, we reobtain the result in [3]. 相似文献
20.
A. B. Al’shin M. A. Istomina 《Computational Mathematics and Mathematical Physics》2006,46(7):1207-1215
The dynamic potential constructed in this paper is used to analyze the existence of a classical solution to the Neumann problem for a Sobolev equation. 相似文献