In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of ...In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).展开更多
This paper deals with an initial-boundary value problem of a fourth-order parabolic equation involving Logarithmic type p-Laplacian,which could be proposed as a model for the epitaxial growth of thin films.By using th...This paper deals with an initial-boundary value problem of a fourth-order parabolic equation involving Logarithmic type p-Laplacian,which could be proposed as a model for the epitaxial growth of thin films.By using the variational method and the logarithmic type Sobolev inequality,we give some threshold results for blow-up solutions and global solutions,which could be classified by the initial energy.The asymptotic estimates about blow-up time and decay estimate of weak solutions are obtained.展开更多
本文讨论非线性Klein-Gordon 方程的混合问题{u(■)—△u+u=F(u,Du,D_xDu) (t,x)∈(0,T)×Ωu(0,x)=h(x) u_t(0,x)=g(x),x∈Ω■u/■v=0■在F(u,Du,D_xDu)≥p sum from i=1 to n u_(X_i)~2+qu_t^2+u 这里(p>0,q>0) 及■_■■^...本文讨论非线性Klein-Gordon 方程的混合问题{u(■)—△u+u=F(u,Du,D_xDu) (t,x)∈(0,T)×Ωu(0,x)=h(x) u_t(0,x)=g(x),x∈Ω■u/■v=0■在F(u,Du,D_xDu)≥p sum from i=1 to n u_(X_i)~2+qu_t^2+u 这里(p>0,q>0) 及■_■■^(ph)(x)×g(x)dx>0时,得到该问题的解在有限时间内爆破.展开更多
基金supported by the Zhejiang Provincial Natural Science Foundation of China(LY21A010016)the National Natural Science Foundation of China(11901550).
文摘In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).
基金Supported by Shandong Provincial Natural Science Foundation of China(Grant No.ZR2021MA003).
文摘This paper deals with an initial-boundary value problem of a fourth-order parabolic equation involving Logarithmic type p-Laplacian,which could be proposed as a model for the epitaxial growth of thin films.By using the variational method and the logarithmic type Sobolev inequality,we give some threshold results for blow-up solutions and global solutions,which could be classified by the initial energy.The asymptotic estimates about blow-up time and decay estimate of weak solutions are obtained.
文摘本文讨论非线性Klein-Gordon 方程的混合问题{u(■)—△u+u=F(u,Du,D_xDu) (t,x)∈(0,T)×Ωu(0,x)=h(x) u_t(0,x)=g(x),x∈Ω■u/■v=0■在F(u,Du,D_xDu)≥p sum from i=1 to n u_(X_i)~2+qu_t^2+u 这里(p>0,q>0) 及■_■■^(ph)(x)×g(x)dx>0时,得到该问题的解在有限时间内爆破.
