共查询到20条相似文献,搜索用时 0 毫秒
1.
Simona Dabuleanu 《Journal of Evolution Equations》2005,5(1):35-60
We study the weak solvability of viscous Hamilton-Jacobi equation:
\,0,\,x\,\in\,\Omega,$" align="middle" border="0">
with Neumann boundary condition and irregular initial data 0. The domain
is a bounded open set and p > 0. The last part deals with the case a convex set and the initial data 0 = in a open set D such that
and
相似文献
2.
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
3.
Jiaqing Pan 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(15):5069-5080
This work studies the large time behavior of free boundary and continuous dependence on nonlinearity for the Cauchy problem of a degenerate parabolic partial differential equation with absorption. Our objective is to give an explicit expression of speed of propagation of the solution and to show that the solution depends on the nonlinearity of the equation continuously. 相似文献
4.
Christian Stinner 《Journal of Differential Equations》2010,248(2):209-228
This paper deals with weak solutions of the one-dimensional viscous Hamilton-Jacobi equation
5.
The growth of the Lm-norm, m [1,], of non-negative solutions to the Cauchy problem t u – u = |u| is studied for non-negative initial data decaying at infinity. More precisely, the function
is shown to be bounded from above and from below by positive real numbers. This result indicates an asymptotic behaviour dominated by the hyperbolic Hamilton-Jacobi term of the equation. A one-sided estimate for ln u is also established. 相似文献
6.
L.E. Payne 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(4):971-1014
This paper deals with the blow-up of the solution to a semilinear second-order parabolic equation with nonlinear boundary conditions. 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
7.
Tor A. Kwembe 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3162-3170
In this paper we consider a semilinear equation with a generalized Wentzell boundary condition. We prove the local well-posedness of the problem and derive the conditions of the global existence of the solution and the conditions for finite time blow-up. We also derive an estimate for the blow-up time. 相似文献
8.
In this paper we study a simple non-local semilinear parabolic equation in a bounded domain with Neumann boundary conditions. We obtain a global existence result for initial data whose L∞-norm is less than a constant depending explicitly on the geometry of the domain. A natural energy is associated to the equation and we establish a relationship between the finite-time blow up of solutions and the negativity of their energy. The proof of this result is based on a Gamma-convergence technique. 相似文献
9.
We consider the problem
in a smooth boundary domain
, as well
as the corresponding evolution equation
. For the stationary equation
we show existence results, then we adapt the techniques of doubling of variables
to the case of the homogeneous Neumann boundary conditions and obtain the
appropriate L
1
-contraction principle and uniqueness. Subsequently, we are able to apply the
nonlinear semigroup theory and prove the L
1
-contraction principle for the associated evolution equation. 相似文献
10.
Noriko Mizoguchi 《Journal of Differential Equations》2003,193(1):212-238
Let p>1 and Ω be a smoothly bounded domain in . This paper is concerned with a Cauchy-Neumann problem
11.
The purpose of the paper is to study properties of solutions of the Cauchy problem for the equation
under the assumption
.
General selfsimilar solutions are constructed. Moreover, for initial data with some decay at infinity, we determine
the leading term of the asymptotics of solutions in
which is described by either solutions of the linear heat equation or by particular selfsimilar solutions of the original equation. 相似文献
12.
In this paper, an initial boundary value problem related to the equation
13.
We investigate the large-time behavior of classical solutions to the thin-film type equation ut=−x(uuxxx). It was shown in previous work of Carrillo and Toscani that for non-negative initial data u0 that belongs to H1(R) and also has a finite mass and second moment, the strong solutions relax in the L1(R) norm at an explicit rate to the unique self-similar source type solution with the same mass. The equation itself is gradient flow for an energy functional that controls the H1(R) norm, and so it is natural to expect that one should also have convergence in this norm. Carrillo and Toscani raised this question, but their methods, using a different Lyapunov functions that arises in the theory of the porous medium equation, do not directly address this since their Lyapunov functional does not involve derivatives of u. Here we show that the solutions do indeed converge in the H1(R) norm at an explicit, but slow, rate. The key to establishing this convergence is an asymptotic equipartition of the excess energy. Roughly speaking, the energy functional whose dissipation drives the evolution through gradient flow consists of two parts: one involving derivatives of u, and one that does not. We show that these must decay at related rates—due to the asymptotic equipartition—and then use the results of Carrillo and Toscani to control the rate for the part that does not depend on derivatives. From this, one gets a rate on the dissipation for all of the excess energy. 相似文献
14.
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
15.
In this paper we consider a heat equation with nonlinear boundary condition occurring in population genetics, the selection–migration problem for alleles in a region, considering flow of genes throughout the boundary. Such a problem determines a gradient flow in a convenient phase space and then the dynamics for large times depends heavily on the knowledge of the equilibrium solutions. We address the questions of the existence of a nontrivial equilibrium solution and its regularity. 相似文献
16.
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
17.
Giuseppe Toscani 《Journal of Evolution Equations》2005,5(2):185-203
We study the large–time behavior of the second moment (energy)
for the flow of a gas in a N-dimensional porous medium with initial density v0(x) 0. The density v(x, t) satisfies the nonlinear degenerate parabolic equation vt = vm where m > 1 is a physical constant. Assuming that
for some > 0, we prove that E(t) behaves asymptotically, as t , like the energy EB(t) of the Barenblatt-Pattle solution B(|x|, t). This is shown by proving that E(t)/EB(t) converges to 1 at the (optimal) rate t–2/(N(m-1)+2). A simple corollary of this result is a central limit theorem for the scaled solution E(t)N/2v(E(t)1/2x, t). 相似文献
18.
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.
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19.
Jinghua Wang 《Journal of Differential Equations》2003,189(1):1-16
In this paper, we study a generalized Burgers equation ut+(u2)x=tuxx, which is a non-uniformly parabolic equation for t>0. We show the existence and uniqueness of classical solutions to the initial-value problem of the generalized Burgers equation with rough initial data belonging to . 相似文献
20.
THEBLOW┐UPPROPERTYFORASYSTEMOFHEATEQUATIONSWITHNONLINEARBOUNDARYCONDITIONSLINZHIGUI,XIECHUNHONGANDWANGMINGXINAbstract.Thispap... 相似文献