The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtai...The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtained.展开更多
This article investigates the blow-up results for the initial boundary value problem to the quasi-linear parabolic equation with p-Laplacian■where p≥2 and the function f(u)satisfies■for some positive constantsα,β...This article investigates the blow-up results for the initial boundary value problem to the quasi-linear parabolic equation with p-Laplacian■where p≥2 and the function f(u)satisfies■for some positive constantsα,β,γwith 0<■,which has been studied under the initial condition Jp(u0)<0.This paper generalizes the above results on the following aspects:a new blow-up condition is given,which holds for all p>2;a new blow-up condition is given,which holds for p=2;some new lifespans and upper blow-up rates are given under certain conditions.展开更多
Let Q_N be an N-anisotropic Laplacian operator, which contains the ordinary Laplacian operator,N-Laplacian operator and the anisotropic Laplacian operator. We firstly obtain the properties of Q_N, which contain the we...Let Q_N be an N-anisotropic Laplacian operator, which contains the ordinary Laplacian operator,N-Laplacian operator and the anisotropic Laplacian operator. We firstly obtain the properties of Q_N, which contain the weak maximal principle, the comparison principle and the mean value property. Then a priori estimates and blow-up analysis for solutions of-Q_(N^u) = Ve^u in bounded domain in R^N, N≥2 are established.Finally, the blow-up behavior of the only singular point is also considered.展开更多
In this paper,we establish the global well-posedness of the stochastic 3D Leray-αmodel with general fractional dissipation driven by multiplicative noise.This model is the stochastic 3D Navier-Stokes equations regula...In this paper,we establish the global well-posedness of the stochastic 3D Leray-αmodel with general fractional dissipation driven by multiplicative noise.This model is the stochastic 3D Navier-Stokes equations regularized through a smoothing kernel of orderθ1 in the nonlinear term and theθ2-fractional Laplacian.In the case ofθ1≥0 andθ2>0 withθ1+θ2≥5/4,we prove the global existence and uniqueness of strong solutions.The main results not only cover many existing works in the deterministic cases,but also generalize some known results of stochastic models such as the stochastic hyperviscous Navier-Stokes equations and classical stochastic3D Leray-αmodel as the special cases.展开更多
In this paper,we consider an initial boundary value problem of m-Laplacian parabolic equation arising in various physical models.We tackle this problem at three different initial energy levels.For the sub-critical ini...In this paper,we consider an initial boundary value problem of m-Laplacian parabolic equation arising in various physical models.We tackle this problem at three different initial energy levels.For the sub-critical initial energy,we obtain the blow-up result and estimate the lower and upper bounds of the blow-up time.For the critical initial energy,we show the global existence,asymptotic behavior,finite time blow-up and the lower bound of the blow-up time.For the sup-critical initial energy,we prove the finite time blow-up and estimate the lower and upper bounds of the blow-up time.展开更多
Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we pro...Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.展开更多
.In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of....In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary.We show the existence of at least one,two or infinitely many non-trivial weak solutions according to hypotheses on given functions.展开更多
We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and singular parabolic inhomogeneous equation of the form ut-△ ∞N u=f, wher...We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and singular parabolic inhomogeneous equation of the form ut-△ ∞N u=f, where An denotes the so-called normalized infinity Laplacian given by △∞ Nu=1/｜Du｜2〈D2uDu,Du〉.展开更多
In this paper, we study the hybrid Schrodinger equation involving normal and fractional Laplace operator, and obtain the existence of the solutions to this class of the hybrid partial differential equation. Our main a...In this paper, we study the hybrid Schrodinger equation involving normal and fractional Laplace operator, and obtain the existence of the solutions to this class of the hybrid partial differential equation. Our main argument is variational methods.展开更多
In this paper, we obtain the existence result of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate parabolic inhomogeneous equation of the form , where denotes infinity Laplacian...In this paper, we obtain the existence result of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate parabolic inhomogeneous equation of the form , where denotes infinity Laplacian given by .展开更多
We establish conditions ensuring either existence or blow-up of nonnegative solutions for the heat equation generated by the Dirichlet fractional Laplacian perturbed by negative potentials on bounded sets. The elabora...We establish conditions ensuring either existence or blow-up of nonnegative solutions for the heat equation generated by the Dirichlet fractional Laplacian perturbed by negative potentials on bounded sets. The elaborated theory is supplied by some examples.展开更多
基金supported by the Fujian Provincial Natural Science Foundation of China (No. Z0511048)
文摘The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtained.
基金Supported by the Doctoral Scientific Research Starting Foundation of Guizhou Normal University of China,2018(No.GZNUD[2018]34 and 11904/0519113).
文摘This article investigates the blow-up results for the initial boundary value problem to the quasi-linear parabolic equation with p-Laplacian■where p≥2 and the function f(u)satisfies■for some positive constantsα,β,γwith 0<■,which has been studied under the initial condition Jp(u0)<0.This paper generalizes the above results on the following aspects:a new blow-up condition is given,which holds for all p>2;a new blow-up condition is given,which holds for p=2;some new lifespans and upper blow-up rates are given under certain conditions.
基金Excellent Young Talent Foundation of Anhui Province (Grant No. 2013SQRL080ZD)
文摘Let Q_N be an N-anisotropic Laplacian operator, which contains the ordinary Laplacian operator,N-Laplacian operator and the anisotropic Laplacian operator. We firstly obtain the properties of Q_N, which contain the weak maximal principle, the comparison principle and the mean value property. Then a priori estimates and blow-up analysis for solutions of-Q_(N^u) = Ve^u in bounded domain in R^N, N≥2 are established.Finally, the blow-up behavior of the only singular point is also considered.
基金supported by National Natural Science Foundation of China(Grant No.12001247)supported by National Natural Science Foundation of China(Grant Nos.12171208,11831014 and 12090011)+2 种基金supported by National Natural Science Foundation of China(Grant Nos.11931004 and 12090011)Natural Science Foundation of Jiangsu Province(Grant No.BK20201019)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘In this paper,we establish the global well-posedness of the stochastic 3D Leray-αmodel with general fractional dissipation driven by multiplicative noise.This model is the stochastic 3D Navier-Stokes equations regularized through a smoothing kernel of orderθ1 in the nonlinear term and theθ2-fractional Laplacian.In the case ofθ1≥0 andθ2>0 withθ1+θ2≥5/4,we prove the global existence and uniqueness of strong solutions.The main results not only cover many existing works in the deterministic cases,but also generalize some known results of stochastic models such as the stochastic hyperviscous Navier-Stokes equations and classical stochastic3D Leray-αmodel as the special cases.
基金Supported by the National Natural Science Foundation of China(Grant No.12271122)the China Postdoctoral Science Foundation(Grant No.2013M540270)the Fundamental Research Funds for the Central Universities。
文摘In this paper,we consider an initial boundary value problem of m-Laplacian parabolic equation arising in various physical models.We tackle this problem at three different initial energy levels.For the sub-critical initial energy,we obtain the blow-up result and estimate the lower and upper bounds of the blow-up time.For the critical initial energy,we show the global existence,asymptotic behavior,finite time blow-up and the lower bound of the blow-up time.For the sup-critical initial energy,we prove the finite time blow-up and estimate the lower and upper bounds of the blow-up time.
基金supported by the Beijing Natural Science Foundation(1212003)。
文摘Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.
文摘.In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary.We show the existence of at least one,two or infinitely many non-trivial weak solutions according to hypotheses on given functions.
基金Supported by National Natural Science Foundation of China(Grant Nos.11071119 and 11171153)
文摘We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and singular parabolic inhomogeneous equation of the form ut-△ ∞N u=f, where An denotes the so-called normalized infinity Laplacian given by △∞ Nu=1/｜Du｜2〈D2uDu,Du〉.
基金supported by the NNSF of China(61563033,11563005)the NSF of Jiangxi Province(20151BAB212011,20151BAB201021)
文摘In this paper, we study the hybrid Schrodinger equation involving normal and fractional Laplace operator, and obtain the existence of the solutions to this class of the hybrid partial differential equation. Our main argument is variational methods.
文摘In this paper, we obtain the existence result of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate parabolic inhomogeneous equation of the form , where denotes infinity Laplacian given by .
文摘We establish conditions ensuring either existence or blow-up of nonnegative solutions for the heat equation generated by the Dirichlet fractional Laplacian perturbed by negative potentials on bounded sets. The elaborated theory is supplied by some examples.
