共查询到20条相似文献,搜索用时 125 毫秒
1.
This paper deals with a nonclassical initial boundary value problem for a two dimensional parabolic equation with Bessel operator. We prove the existence and uniqueness of the weak solution of the given nonlinear problem. We start by solving the associated linear problem. After writing this latter in its operator form, we establish an a priori bound from which we deduce the uniqueness of the strong solution. For the solvability of the associated linear problem, we prove that the range of the operator generated by the considered problem is dense. On the basis of the obtained results of the linear problem, we apply an iterative process to establish the existence and uniqueness of the nonlinear problem. 相似文献
2.
This paper deals with the critical curve of the non-Newtonian polytropic filtration equation coupled via nonlinear boundary flux. The critical global existence curve is obtained by constructing various self-similar supersolutions and subsolutions. Furthermore, we get some new results on the critical Fujita curve. 相似文献
3.
We consider an Allen-Cahn type equation of the form ut=Δu+ε−2fε(x,t,u), where ε is a small parameter and fε(x,t,u)=f(u)−εgε(x,t,u) a bistable nonlinearity associated with a double-well potential whose well-depths can be slightly unbalanced. Given a rather general initial data u0 that is independent of ε, we perform a rigorous analysis of both the generation and the motion of interface. More precisely we show that the solution develops a steep transition layer within the time scale of order ε2|lnε|, and that the layer obeys the law of motion that coincides with the formal asymptotic limit within an error margin of order ε. This is an optimal estimate that has not been known before for solutions with general initial data, even in the case where gε≡0.Next we consider systems of reaction-diffusion equations of the form
4.
5.
6.
We investigate the non-existence of solutions to a class of evolution inequalities; in this case, as it happens in a relatively small number of blow-up studies, nonlinearities depend also on time-variable t and spatial derivatives of the unknown. The present results, which in great part do not require any assumption on the regularity of data, are completely new and shown with various applications. Some of these results referring to the problem ut=Δu+a(x)|u|p+λf(x) in RN, t>0 include the non-existence results of positive global solutions obtained by Fujita and others when a≡1 and f≡0, Bandle-Levine and Levine-Meier when a≡|x|m and f≡0, Pinsky when either f≡0 or f?0 and λ>0, Zhang and Bandle-Levine-Zhang when a≡1 and λ=1. 相似文献
7.
Xianfa Song Sining Zheng Zhaoxin Jiang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(1):1-10
This paper deals with a nonlinear diffusion system coupled via nonlinear reaction terms of power type. As results of interactions among the multi-nonlinearities in the system described by six exponents, global boundedness and blow-up criteria of positive solutions are determined.Supported by the National Natural Science Foundation of China.Received: December 12, 2001; revised: May 6, December 3, 2002 相似文献
8.
The problem of identifying the coefficient in a square porous medium is considered. It is shown that under certain conditions of data f,g, and for a properly specified class A of admissible coefficients, there exists at least one a∈A such that (a,u) is a solution of the corresponding inverse problem. 相似文献
9.
Zhongping Li Chunlai Mu Zejian Cui 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(2):284-298
This paper deals with the critical curves of the fast diffusive polytropic filtration equations coupled via nonlinear boundary
flux. By constructing self-similar super and sub solutions we obtain the critical global existence curve. The critical curve
of Fujita type is conjectured with the aid of some new results.
相似文献
10.
Travelling front solution for a class of competition-diffusion system with high-order singular point
In this paper, the existence of travelling front solution for a class of competition-diffusion system with high-order singular
point
is studied, where d
i,ai>0 (i=1,2) and w=(w
1(x,t),w
2(x,t)). Under the certain assumptions on f, it is showed that if a
i<1 for some i, then (1) has no travelling front solution, if a
i≥1 for i=1,2, then there is a c
0,c*>0, where c* is called the minimal wave speed of (I), such that if c≥c
0 or c=c*, then (I) has a travelling front solution, if c<c*, then (I) has no travelling front solution by using the shooting method in combination with a compactness argument.
Project supported by both the National (49772161) and Henan Province (984050300) Natural Science Foundations of China. 相似文献
(I) |
11.
Adrien Blanchet 《Journal of Differential Equations》2006,231(2):656-672
This paper is devoted to regularity results and geometric properties of the singular set of the parabolic obstacle problem with variable right-hand side. Making use of a monotonicity formula for singular points, we prove the uniqueness of blow-up limits at singular points. These results apply to parabolic obstacle problem with variable coefficients. 相似文献
12.
13.
L.M. Bragança 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):2991-3003
We investigate some well-posedness issues for the initial value problem (IVP) associated with the system
14.
In this paper, we consider the existence and non-existence of global solutions of the non-Newtonian polytropic filtration equations with nonlinear boundary conditions. We first obtain the critical global existence curve by constructing various self-similar supersolutions and subsolutions. And then the critical Fujita curve is conjectured with the aid of some new results. 相似文献
15.
In this paper we prove the local and global well-posedness of a dissipative nonlinear electrohydrodynamic system in modulation spaces under certain conditions of s, q, and σ. 相似文献
16.
Flávio Dickstein Miguel Loayza 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(1):1-23
We consider the Cauchy problem for the weakly coupled parabolic system ∂
t
w
λ−Δ w
λ = F(w
λ) in R
N
, where λ > 0, w
λ = (u
λ, v
λ), F(w
λ) = (v
λ
p
, u
λ
q
) for some p, q ≥ 1, pq > 1, and , for some nonnegative functions φ1, φ2
C
0(R
N
). If (p, q) is sub-critical or either φ1 or φ2 has slow decay at ∞, w
λ blows up for all λ > 0. Under these conditions, we study the blowup of w
λ for λ small.
相似文献
17.
Raúl Ferreira Arturo de Pablo Fernando Quirós Julio D. Rossi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(4):586-594
We study the solutions of a parabolic system of heat equations coupled at the boundary through a nonlinear flux. We characterize
in terms of the parameters involved when non-simultaneous quenching may appear. Moreover, if quenching is non-simultaneous
we find the quenching rate, which surprisingly depends on the flux associated to the other component.
Partially supported by project BFM2002-04572 (Spain).
Partially supported by UBA grant EX046, CONICET and Fundación Antorchas (Argentina).
Received: February 17, 2004; revised: July 5, 2004 相似文献
18.
THEBLOW┐UPPROPERTYFORASYSTEMOFHEATEQUATIONSWITHNONLINEARBOUNDARYCONDITIONSLINZHIGUI,XIECHUNHONGANDWANGMINGXINAbstract.Thispap... 相似文献
19.
We consider a hyperbolic version of Eells-Sampson's equation:
. This equation is semilinear with respect to space derivative and time derivative. Letu
(x) be the solution with initial data u(0) and
(0), and putv
(t,x)=u
(t,x). We show that when the resistance ,V
(t,x) converges to a solution of the original parabolic Eells-Sampson's equation:
. Note thatv
t(0)=
(0) diverges when . We show that this phenomena occurs in more general situations.This article was processed by the author using the Springer-Verlag
Pjourlg macro package. 相似文献
20.
This paper studies heat equations with inner absorptions and coupled boundary fluxes of mixed-type nonlinearities. At first, the critical exponent is obtained, and simply described via a characteristic algebraic system introduced by us. Then, as the main results of the paper, three blow-up rates are established under different dominations of nonlinearities for the one-dimensional case, and represented in another characteristic algebraic system. In particular, it is observed that unlike those in previous literature on parabolic models with absorptions, two of the multiple blow-up rates obtained here do depend on the absorption exponents. In the known works, the absorptions affect the blow-up criteria, the blow-up time, as well as the initial data required for the blow-up of solutions, all without changing the blow-up rates. To our knowledge, this is the first example of absorption-dependent blow-up rates, exploiting the significant interactions among diffusions, inner absorptions and nonlinear boundary fluxes in the coupled system. It is also proved that the blow-up of solutions in the model occurs on the boundary only. 相似文献