共查询到20条相似文献,搜索用时 15 毫秒
1.
Thierry Cazenave Flávio Dickstein Fred B. Weissler 《Nonlinear Analysis: Theory, Methods & Applications》2008
In this paper, we prove sharp blow up and global existence results for a heat equation with nonlinear memory. It turns out that the Fujita critical exponent is not the one which would be predicted from the scaling properties of the equation. 相似文献
2.
Christian Stinner 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(5):1945-1959
We study nonnegative solutions to the Cauchy problem for a semilinear parabolic equation with a nonlinearity which is critical in the sense of Joseph and Lundgren. We establish the rate of convergence to zero of solutions that start from initial data which are near the singular steady state. In the critical case, this rate contains a logarithmic term which does not appear in the supercritical case and makes the calculations more delicate. 相似文献
3.
J. Chabrowski 《Journal of Fixed Point Theory and Applications》2007,2(2):333-352
We investigate the solvability of the Neumann problem involving the critical Sobolev exponent, the Hardy potential and a nonlinear
term of lower order. Lower order terms are allowed to interfere with the spectrum of the operator subject to the Neumann boundary conditions. Solutions are obtained via a min-max procedure based on the variational mountain-pass
principle and topological linking.
相似文献
4.
We consider the blowup rate of solutions for a semilinear heat equation
5.
We consider two-dimensional mixed problems in an exterior domain for a semilinear strongly damped wave equation with a power-type nonlinearity |u|p. If the initial data have a small weighted energy, we shall derive a global existence and energy decay results in the case when the power p of the nonlinear term satisfies p>6. 相似文献
6.
7.
We study the existence and nonexistence of positive (super)solutions to the nonlinear p-Laplace equation
8.
Fei Liang 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):2189-2198
This paper deals with the blow-up for a system of semilinear r-Laplace heat equations with nonlinear boundary flux. It is shown that, under certain conditions on the nonlinearities and data, blow-up will occur at some finite time, and when blow-up does occur upper and lower bounds for the blow-up time are obtained. 相似文献
9.
Lei Wei 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1739-1746
In this work, we consider semilinear elliptic equations with boundary blow-up whose nonlinearities involve a negative exponent. Combining sub- and super-solution arguments, comparison principles and topological degree theory, we establish the existence of large solutions. Furthermore, we show the existence of a maximal large positive solution. 相似文献
10.
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
11.
12.
THEBLOW┐UPPROPERTYFORASYSTEMOFHEATEQUATIONSWITHNONLINEARBOUNDARYCONDITIONSLINZHIGUI,XIECHUNHONGANDWANGMINGXINAbstract.Thispap... 相似文献
13.
We consider a one-dimensional semilinear parabolic equation , for which the spatial derivative of solutions becomes unbounded in finite time while the solutions themselves remain bounded. We establish estimates of blowup rate upper and lower bounds. We prove that in this case the blowup rate does not match the one obtained by the rescaling method. 相似文献
14.
Parabolic equations with nonlinear singularities 总被引:2,自引:0,他引:2
15.
We show that the solutions of a semilinear system of elastic waves in an exterior domain with a localized damping near infinity decay in an algebraic rate to zero. We impose an additional condition on the Lamé coefficients. It seems that this restriction cannot be overcome by using the two-finite-speed propagation of the elastic model, since we do not assume compact support on the initial data and because the dissipation does not have compact support. The decay rates obtained for the total energy of the linear problem and the L2-norm of the solution improve previous results. For the semilinear problem the decay rates in this paper seem to be the first contribution, mainly in the context of initial data without compact support and localized dissipation. 相似文献
16.
Yang Cao 《Journal of Differential Equations》2009,246(12):4568-4590
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
17.
Blow-up for semilinear parabolic equations with nonlinear memory 总被引:4,自引:0,他引:4
In this paper, we consider the semilinear parabolic
equation
with homogeneous Dirichlet boundary conditions, where
p, q are
nonnegative constants. The blowup criteria and the blowup rate
are obtained. 相似文献
18.
Catherine Bandle 《Journal of Differential Equations》2011,251(8):2143-827
It is well known that the heat kernel in the hyperbolic space has a different behavior for large times than the one in the Euclidean space. The main purpose of this paper is to study its effect on the positive solutions of Cauchy problems with power nonlinearities. Existence and non-existence results for local solutions are derived. Emphasis is put on their long time behavior and on Fujita?s phenomenon. To have the same situation as for the Cauchy problem in RN, namely finite time blow up for all solutions if the exponent is smaller than a critical value and existence of global solutions only for powers above the critical exponent, we must introduce a weight depending exponentially on the time. In this respect the situation is similar to problems in bounded domains with Dirichlet boundary conditions. Important tools are estimates for the heat kernel in the hyperbolic space and comparison principles. 相似文献
19.
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
20.
Michinori Ishiwata 《Journal of Differential Equations》2010,249(6):1466-1482
This paper is concerned with a semilinear parabolic equation involving critical Sobolev exponent in a ball or in RN. The asymptotic behavior of unbounded, radially symmetric, nonnegative global solutions which do not decay to zero is given. The structure of the space of initial data is also discussed. 相似文献