共查询到20条相似文献,搜索用时 578 毫秒
1.
Hui-ling LI & Ming-xin WANG Department of Mathematics Southeast University Nanjing China 《中国科学A辑(英文版)》2007,50(4):590-608
This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vazquez and the comparison principle, we deduce that the blow-up occurs only on the boundary (?)Ω. In addition, for a bounded Lipschitz domainΩ, we establish the blow-up rate estimates for the positive solution to this problem with a= 0. 相似文献
2.
3.
This paper deals with propagations of singularities in solutions to a parabolic system coupled with nonlocal nonlinear sources.
The estimates for the four possible blow-up rates as well as the boundary layer profiles are established. The critical exponent
of the system is determined also.
This work was supported by the National Natural Science Foundation of China (Grant No. 10771024) 相似文献
4.
In this note, we prove the partial regularity of stationary weak solutions for the Landau-Lifshitz system with general potential
in four or three dimensional space. As well known, in general, since the constraint of the methods, in order to get the partial
regularity of stationary weak solution of the Landau-Lifshitz system with potential, we need to add some very strongly conditions
on the potential. The main difficulty caused by potential is how to find the equation satisfied by the scaling function, which
breaks down the blow-up processing. We estimate directly Morrey’s energy to avoid the difficulties by blowing up.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10631020, 60850005) and the Natural Science
Foundation of Zhejiang Province (Grant No. D7080080) 相似文献
5.
Shi Hui Zhu 《数学学报(英文版)》2015,31(3):411-429
We study the blow-up solutions for the Davey–Stewartson system(D–S system, for short)in L2x(R2). First, we give the nonlinear profile decomposition of solutions for the D–S system. Then, we prove the existence of minimal mass blow-up solutions. Finally, by using the characteristic of minimal mass blow-up solutions, we obtain the limiting profile and a precisely mass concentration of L2 blow-up solutions for the D–S system. 相似文献
6.
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
7.
Yong Zhou 《Journal of Functional Analysis》2007,250(1):227-248
In this paper, firstly we find best constants for two convolution problems on the unit circle via a variational method. Then we apply the best constants on a nonlinear integrable shallow water equation (the DGH equation) to give sufficient conditions on the initial data, which guarantee finite time singularity formation for the corresponding solutions. Finally, we discuss the blow-up phenomena for the nonperiodic case. 相似文献
8.
J. S. Pang 《Journal of Optimization Theory and Applications》1990,66(1):121-135
In this paper, we derive some further differentiability properties of solutions to a parametric variational inequality problem defined over a polyhedral set. We discuss how these results can be used to establish the feasibility of continuation of Newton's method for solving the variational problem in question.This work was based on research supported by the National Science Foundation under Grant No. ECS-87-17968. 相似文献
9.
The blow-up solutions of the Cauchy problem for the Davey-Stewartson system, which is a model equation in the theory of shallow water waves, are investigated. Firstly, the existence of the ground state for the system derives the best constant of a Gagliardo-Nirenberg type inequality and the variational character of the ground state. Secondly, the blow-up threshold of the Davey-Stewartson system is developed in R3. Thirdly, the mass concentration is established for all the blow-up solutions of the system in R2. Finally, the existence of the minimal blow-up solutions in R2 is constructed by using the pseudo-conformal invariance. The profile of the minimal blow-up solutions as t→T (blow-up time) is in detail investigated in terms of the ground state. 相似文献
10.
In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions. 相似文献
11.
This paper discusses nonlinear SchrSdinger equation with a harmonic potential. By constructing a different cross-constrained variational problem and the so-called invariant sets, we derive a new threshold for blow-up and global existence of solutions. 相似文献
12.
13.
In this paper we study finite time blow-up of solutions
of a hyperbolic model for chemotaxis. Using appropriate scaling
this hyperbolic model leads to a parabolic model as studied by
Othmer and Stevens (1997) and Levine and Sleeman (1997). In the
latter paper, explicit solutions which blow-up in finite time were
constructed. Here, we adapt their method to construct a
corresponding blow-up solution of the hyperbolic model. This
construction enables us to compare the blow-up times of the
corresponding models. We find that the hyperbolic blow-up is
always later than the parabolic blow-up. Moreover, we show that
solutions of the hyperbolic problem become negative near blow-up.
We calculate the zero-turning-rate time explicitly and we show
that this time can be either larger or smaller than the parabolic
blow-up time.
The blow-up models as discussed here and elsewhere are limiting
cases of more realistic models for chemotaxis. At the end of the
paper we discuss the relevance to biology and exhibit numerical
solutions of more realistic models. 相似文献
14.
In this paper we study finite time blow-up of solutions
of a hyperbolic model for chemotaxis. Using appropriate scaling
this hyperbolic model leads to a parabolic model as studied by
Othmer and Stevens (1997) and Levine and Sleeman (1997). In the
latter paper, explicit solutions which blow-up in finite time were
constructed. Here, we adapt their method to construct a
corresponding blow-up solution of the hyperbolic model. This
construction enables us to compare the blow-up times of the
corresponding models. We find that the hyperbolic blow-up is
always later than the parabolic blow-up. Moreover, we show that
solutions of the hyperbolic problem become negative near blow-up.
We calculate the zero-turning-rate time explicitly and we show
that this time can be either larger or smaller than the parabolic
blow-up time.
The blow-up models as discussed here and elsewhere are limiting
cases of more realistic models for chemotaxis. At the end of the
paper we discuss the relevance to biology and exhibit numerical
solutions of more realistic models. 相似文献
15.
Existence and uniqueness of strong solutions of stochastic partial differential equations of parabolic type with reflection (e.g., the solutions are never allowed to be negative) is proved. The problem is formulated as a stochastic variational inequality and then compactness is used to derive the result, but the method requires the space dimension to be one.This research was supported by NSERC under Grant No. 8051. 相似文献
16.
We study equimultiple deformations of isolated hypersurface singularities, introduce a blow-up equivalence of singular points,
which is intermediate between topological and analytic ones, and give numerical sufficient conditions for the blow-up versality
of the equimultiple deformation of a singularity or multisingularity induced by the space of algebraic hypersurfaces of a
given degree. For singular points, which become Newton nondegenerate after one blowing up, we prove that the space of algebraic
hypersurfaces of a given degree induces all the equimultiple deformations (up to the blow-up equivalence) which are stable
with respect to removing monomials lying above the Newton diagrams. This is a generalization of a theorem by B. Chevallier.
This work was partially supported by Grant No.6836-1-9 of the Israeli Ministry of Sciences. The second author thanks the Max-Planck
Institut (Bonn) for hospitality and financial support. 相似文献
17.
We obtain a blow-up result for solutions to a semi-linear wave equation with scale-invariant dissipation and mass and power non-linearity, in the case in which the model has a “wave like” behavior. We perform a change of variables that transforms our starting equation in a strictly hyperbolic semi-linear wave equation with time-dependent speed of propagation. Applying Kato's lemma we prove a blow-up result for solutions to the transformed equation under some assumptions on the initial data. The limit case, that is, when the exponent p is exactly equal to the upper bound of the range of admissible values of p yielding blow-up needs special considerations. In this critical case an explicit integral representation formula for solutions of the corresponding linear Cauchy problem in 1d is derived. Finally, carrying out the inverse change of variables we get a non-existence result for global (in time) solutions to the original model. 相似文献
18.
We study blow-up, global existence and ground state solutions for the N-coupled focusing nonlinear SchrSdinger equations. Firstly, using the Nehari manifold approach and some variational techniques, the existence of ground state solutions to the equations (CNLS) is established. Secondly, under certain conditions, finite time blow-up phenomena of the solutions is derived. Finally, by introducing a refined version of compactness lemma, the L2 concentration for the blow-up solutions is obtained. 相似文献
19.
This work is devoted to the solvability and finite time blow-up of solutions of the Cauchy problem for the dissipative Boussinesq equation in all space dimension. We prove the existence and uniqueness of local mild solutions in the phase space by means of the contraction mapping principle. By establishing the time-space estimates of the corresponding Green operators, we obtain the continuation principle. Under some restriction on the initial data, we further study the results on existence and uniqueness of global solutions and finite time blow-up of solutions with the initial energy at three different level. Moreover, the sufficient and necessary conditions of finite time blow-up of solutions are given. 相似文献
20.
This article discusses the weakly coupled non-linear Schrödinger equations. With the variational characterization of the ground state solutions, the potential well argument and the concavity method, we derive a sharp condition for blow-up and global existence to the solutions of the Cauchy problem. At the same time, we also prove the instability of standing waves. 相似文献