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1.
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   

2.
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   

3.
Motivated by a recent curvature flow introduced by Professor S.-T. Yau [S.-T. Yau, Private communication on his “Curvature Difference Flow”, 2007], we use a simple curvature flow to evolve a convex closed curve to another one (under the assumption that both curves have the same length). We show that, under the evolution, the length is preserved and if the curvature is bounded above during the evolution, then an initial convex closed curve can be evolved to another given one.  相似文献   

4.
Bandle et al. [1] obtained a quite interesting result about a semilinear heat equation that the Fujita exponent relative to the whole hyperbolic space is just the same as that relative to bounded domain in Euclidean space, and, in addition, the properties of solutions are different in the critical exponent case. Our purpose is to answer an open problem proposed by Bandle et al. for the critical exponent case, and it, together with the one obtained by them, shows that the critical exponent case does belong to the non-blow-up case, which is completely different from the case in Euclidean space.  相似文献   

5.
In this paper, we study the properties of solutions to a degenerate parabolic equation with variable density and absorption. We first obtain a critical exponent, which distinguishes the localization of solutions from the positivity of them. When positivity prevails, we obtain the other critical exponent with respect to the decay of the variable density, which separates the global existence of interfaces from the disappearance of them. Moreover, the long time behavior of interfaces is characterized.  相似文献   

6.
This paper deals with the exterior problem of the Newtonian filtration equation with nonlinear boundary sources. The large time behavior of solutions including the critical Fujita exponent are determined or estimated. An interesting phenomenon is illustrated that there exists a threshold value for the coefficient of the lower order term, which depends on the spacial dimension. Exactly speaking, the critical global exponent is strictly less than the critical Fujita exponent when the coefficient is under this threshold, while these two exponents are identically equal when the coefficient is over this threshold. Supported by the NNSF of China and the China Postdoctoral Science Foundation.  相似文献   

7.
In this paper, we discuss the critical exponents and non-extinction property for a nonlinear boundary value problem of a fast diffusive polytropic filtration equation.  相似文献   

8.
We show that a nontrivial homothetic self-similar solution can happen only when F(k)=kα or F(k)=−kα. We also derive a parametric representation of a translational self-similar solution. A translational self-similar solution may have self-intersections but cannot be a simple closed curve for any F(k).  相似文献   

9.
This paper is concerned with the existence of ground states for the Schrödinger-Poisson equation , where V(u) is a Hartree type nonlinearity, stemming from the coupling with the Poisson equation, which includes the so-called doping profile or impurities. By means of variational methods in the energy space we show that ground states exist and belong to the Schwartz space of rapidly decreasing functions whenever total charge not exceed some critical value, it is also shown that for values of the total charge greater than this critical value, energy is not bounded from below. In addition, we show that this critical value is the total charge given by the impurities.  相似文献   

10.
This paper concerns with the Cauchy problems of semilinear pseudo-parabolic equations. After establishing the necessary existence, uniqueness and comparison principle for mild solutions, which are also classical ones provided that the initial data are appropriately smooth, we investigate large time behavior of solutions. It is shown that there still exist the critical global existence exponent and the critical Fujita exponent for pseudo-parabolic equations and that these two critical exponents are consistent with the corresponding semilinear heat equations.  相似文献   

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