共查询到20条相似文献,搜索用时 31 毫秒
1.
We consider the optimization problem of minimizing with a constraint on the volume of {u>0}. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution u is locally Lipschitz continuous and that the free boundary, ∂{u>0}∩Ω, is smooth. 相似文献
2.
The Randić index R(G) of a graph G is defined by , where d(u) is the degree of a vertex u in G and the summation extends over all edges uv of G. A conjecture about the Randić index says that for any triangle-free graph G of order n with minimum degree δ≥k≥1, one has , where the equality holds if and only if G=Kk,n−k. In this short note we give a confirmative proof for the conjecture. 相似文献
3.
Blow-up analysis for a system of heat equations with nonlinear flux which obey different laws 总被引:1,自引:0,他引:1
We consider a system of heat equations ut=Δu and vt=Δv in Ω×(0,T) completely coupled by nonlinear boundary conditions We prove that the solutions always blow up in finite time for non-zero and non-negative initial values. Also, the blow-up only occurs on ∂Ω with for p,q>0, 0≤α<1 and 0≤β<p. 相似文献
4.
We consider the following nonlinear elliptic equation with singular nonlinearity: where α>β>1, a>0, and Ω is an open subset of , n2. Let uH1(Ω) with and be a nonnegative stationary solution. If we denote the zero set of u by we shall prove that the Hausdorff dimension of Σ is less than or equal to . 相似文献
5.
We consider an aggregation equation in , d2, with fractional dissipation: ut+(uK*u)=−νΛγu, where ν0, 0<γ<1, and K(x)=e−|x|. We prove a refined blowup criteria by which the global existence of solutions is controlled by its norm, for any . We prove the finite time blowup of solutions for a general class of nonsymmetric initial data. The argument presented works for both the inviscid case ν=0 and the supercritical case ν>0 and 0<γ<1. Additionally, we present new proofs of blowup which does not use free energy arguments. 相似文献
6.
In this paper we study the Cauchy problem for the semilinear fractional power dissipative equation ut+(−Δ)αu=F(u) for the initial data u0 in critical Besov spaces with , where α>0, F(u)=P(D)ub+1 with P(D) being a homogeneous pseudo-differential operator of order d[0,2α) and b>0 being an integer. Making use of some estimates of the corresponding linear equation in the frame of mixed time–space spaces, the so-called “mono-norm method” which is different from the Kato's “double-norm method,” Fourier localization technique and Littlewood–Paley theory, we get the well-posedness result in the case . 相似文献
7.
We investigate the following modification of the well-known irregularity strength of graphs. Given a total weighting w of a graph G=(V,E) with elements of a set {1,2,…,s}, denote wtG(v)=∑evw(e)+w(v) for each vV. The smallest s for which exists such a weighting with wtG(u)≠wtG(v) whenever u and v are distinct vertices of G is called the total vertex irregularity strength of this graph, and is denoted by . We prove that for each graph of order n and with minimum degree δ>0. 相似文献
8.
Igor E. Zverovich 《Journal of Algorithms in Cognition, Informatics and Logic》2006,58(2):118-133
A proper k-coloring C1,C2,…,Ck of a graph G is called strong if, for every vertex uV(G), there exists an index i{1,2,…,k} such that u is adjacent to every vertex of Ci. We consider classes of strongly k-colorable graphs and show that the recognition problem of is NP-complete for every k4, but it is polynomial-time solvable for k=3. We give a characterization of in terms of forbidden induced subgraphs. Finally, we solve the problem of uniqueness of a strong 3-coloring. 相似文献
9.
Nonradial large solutions of sublinear elliptic problems 总被引:1,自引:0,他引:1
Khalifa El Mabrouk Wolfhard Hansen 《Journal of Mathematical Analysis and Applications》2007,330(2):1025-1041
Let p be a nonnegative locally bounded function on , N3, and 0<γ<1. Assuming that the oscillation sup|x|=rp(x)−inf|x|=rp(x) tends to zero as r→∞ at a specified rate, it is shown that the equation Δu=p(x)uγ admits a positive solution in satisfying lim|x|→∞u(x)=∞ if and only if 相似文献
10.
Thierry Cazenave Flvio Dickstein Fred B. Weissler 《Journal of Mathematical Analysis and Applications》2009,360(2):537-547
In this paper, we consider the nonlinear heat equation(NLH)
ut−Δu=|u|αu,