We investigate the initial boundary value problem of some semilinear pseudo-parabolic equations with Newtonian nonlocal term.We establish a lower bound for the blow-up time if blow-up does occur.Also both the upper bo...We investigate the initial boundary value problem of some semilinear pseudo-parabolic equations with Newtonian nonlocal term.We establish a lower bound for the blow-up time if blow-up does occur.Also both the upper bound for T and blow up rate of the solution are given when J(u 0)<0.Moreover,we establish the blow up result for arbitrary initial energy and the upper bound for T.As a product,we refine the lifespan when J(u 0)<0.展开更多
In this paper,the authors study the asymptotically linear elliptic equation on manifold with conical singularities-ΔBu+λu=a(z)f(u),u≥0 in R+N,where N=n+1≥3,λ>0,z=(t,x_(1),…,x_(n)),and ΔB=(t■t)^(2)+■^(2)x_(...In this paper,the authors study the asymptotically linear elliptic equation on manifold with conical singularities-ΔBu+λu=a(z)f(u),u≥0 in R+N,where N=n+1≥3,λ>0,z=(t,x_(1),…,x_(n)),and ΔB=(t■t)^(2)+■^(2)x_(1)+…+■^(2)x_(n).Combining properties of cone-degenerate operator,the Pohozaev manifold and qualitative properties of the ground state solution for the limit equation,we obtain a positive solution under some suitable conditions on a and f.展开更多
基金NSFC(Nos.11811145,12071364)the Fundamental Research Funds for the Central Universities(WUT:2020IA003)Key Scientific Research Foundation of the Higher Education Institutions of Henan Province,China(No.19A110004)。
文摘We investigate the initial boundary value problem of some semilinear pseudo-parabolic equations with Newtonian nonlocal term.We establish a lower bound for the blow-up time if blow-up does occur.Also both the upper bound for T and blow up rate of the solution are given when J(u 0)<0.Moreover,we establish the blow up result for arbitrary initial energy and the upper bound for T.As a product,we refine the lifespan when J(u 0)<0.
基金supported by the National Natural Science Foundation of China(Nos.11631011,11601402,12171183,11831009,12071364,11871387)。
文摘In this paper,the authors study the asymptotically linear elliptic equation on manifold with conical singularities-ΔBu+λu=a(z)f(u),u≥0 in R+N,where N=n+1≥3,λ>0,z=(t,x_(1),…,x_(n)),and ΔB=(t■t)^(2)+■^(2)x_(1)+…+■^(2)x_(n).Combining properties of cone-degenerate operator,the Pohozaev manifold and qualitative properties of the ground state solution for the limit equation,we obtain a positive solution under some suitable conditions on a and f.
