共查询到20条相似文献,搜索用时 31 毫秒
1.
Noriko Mizoguchi 《Journal of Differential Equations》2011,250(1):26-32
A solution u of a Cauchy problem for a semilinear heat equation
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Steven D. Taliaferro 《Journal of Differential Equations》2011,250(2):892-928
We study classical nonnegative solutions u(x,t) of the semilinear parabolic inequalities
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We take up the existence and global behavior of positive continuous solutions of the following nonlinear parabolic equation in (n?2) with boundary conditions u=0 on and u(x,0)=u0(x). The nonlinear term is required to satisfy some conditions related to a functional class , which we introduce in this paper and will be called parabolic Kato class in the half space. Our approach is based on potential theory. 相似文献
4.
Ross G. Pinsky 《Journal of Differential Equations》2006,220(2):407-433
Consider classical solutions u∈C2(Rn×(0,∞))∩C(Rn×[0,∞)) to the parabolic reaction diffusion equation
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Norbert Ortner 《Bulletin des Sciences Mathématiques》2003,127(10):835-843
L. Hörmander's extension of Ásgeirsson's mean value theorem states that if u is a solution of the inhomogeneous ultrahyperbolic equation (Δx−Δy)u=f, , , then
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Markus Biegert 《Journal of Differential Equations》2009,247(7):1949-698
Let Ω⊂RN be a bounded domain and let μ be an admissible measure on ∂Ω. We show in the first part that if Ω has the H1-extension property, then a realization of the Laplace operator with generalized nonlinear Robin boundary conditions, formally given by on ∂Ω, generates a strongly continuous nonlinear submarkovian semigroup SB=(SB(t))t?0 on L2(Ω). We also obtain that this semigroup is ultracontractive in the sense that for every u,v∈Lp(Ω), p?2 and every t>0, one has
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Linghai Zhang 《Journal of Differential Equations》2008,245(11):3470-3502
Let u=u(x,t,u0) represent the global strong/weak solutions of the Cauchy problems for the general n-dimensional incompressible Navier-Stokes equations
9.
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
10.
In this paper we investigate the dynamics of solitons occurring in the nonlinear Schroedinger equation when a parameter h→0.We prove that under suitable assumptions, the soliton approximately follows the dynamics of a point particle, namely, the motion of its barycenterqh(t) satisfies the equation
11.
Parabolic equations with nonlinear singularities 总被引:2,自引:0,他引:2
12.
Michael Winkler 《Journal of Differential Equations》2003,192(2):445-474
We study nonglobal positive solutions to the Dirichlet problem for ut=up(Δu+u) in bounded domains, where 0<p<2. It is proved that the set of points at which u blows up has positive measure and the blow-up rate is exactly . If either the space dimension is one or p<1, the ω-limit set of consists of continuous functions solving . In one space dimension it is shown that actually as t→T, where w coincides with an element of a one-parameter family of functions inside each component of its positivity set; furthermore, we study the size of the components of {w>0} with the result that this size is uniquely determined by Ω in the case p<1, while for p>1, the positivity set can have the maximum possible size for certain initial data, but it may also be arbitrarily close to the minimal length π. 相似文献
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Giuseppe M. Coclite Gisèle R. Goldstein Jerome A. Goldstein 《Journal of Differential Equations》2009,246(6):2434-3971
Of concern is the nonlinear uniformly parabolic problem
16.
We consider a system of two porous medium equations defined on two different components of the real line, which are connected by the nonlinear contact condition
17.
Nguyen Huy Tuan Dang Duc Trong 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1842-1852
Consider a nonlinear backward parabolic problem in the form
18.
Let Ω be a bounded domain in R2, u+=u if u?0, u+=0 if u<0, u−=u+−u. In this paper we study the existence of solutions to the following problem arising in the study of a simple model of a confined plasma
19.
We consider the following nonlinear Schrödinger equations in Rn
20.
Yehuda Pinchover 《Journal of Functional Analysis》2004,206(1):191-209
In this paper we study the large time behavior of the (minimal) heat kernel kPM(x,y,t) of a general time-independent parabolic operator Lu=ut+P(x,∂x)u which is defined on a noncompact manifold M. More precisely, we prove that