In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial s...In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial solutions with negative initial energy will blow up in finite time,and provide an upper bound estimate for the blow-up time.Additionally,we also derive a lower bound estimate for the blow-up time.展开更多
This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the beh...This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the behavior of the coefficients when time variable tends to positive infinity.Moreover,the global existence of solutions are discussed for non-positive exponents.展开更多
We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argum...We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argument by contradiction with the test function techniques,we prove that not only any non-trivial solution blows up in finite time under 0<α<1,N≥1 and p>1,but also any non-trivial solution blows up in finite time underα=0,2≤N≤4 and p being the Strauss exponent.展开更多
In this paper, we consider the two-dimensional incompressible Navier-Stokes-Landau-Lifshitz system. The first result is the classical Serrin-type blow-up criterion for Navier-Stokes-Landau-Lifshitz system whose index ...In this paper, we consider the two-dimensional incompressible Navier-Stokes-Landau-Lifshitz system. The first result is the classical Serrin-type blow-up criterion for Navier-Stokes-Landau-Lifshitz system whose index is the same as Navier-Stokes equation. More generally, we establish the blow-up criterion in the homogenous Besov space with the negative index whose form is analogue to Serrin-type. As a result, the blow-up criterion in BMO space with respect to spatial variable is also attained. These results can be regarded as the extension of the recent work [Math. Methods Appl. Sci. 46, (2023), 2500–2516].展开更多
This paper deals with the blow-up properties of solutions to semilinear heat equation ut-uxx= up in (0, 1) × (0, T) with the Neumann boundary condition ux(0, t) = 0, u:x1, t) = 1 on [0, T). The necessary and suff...This paper deals with the blow-up properties of solutions to semilinear heat equation ut-uxx= up in (0, 1) × (0, T) with the Neumann boundary condition ux(0, t) = 0, u:x1, t) = 1 on [0, T). The necessary and sufficient conditions under which all solutions to have a finite time blow-up and the exact blow-up rates are established. It is proved that the blow-up will occur only at the boundary x = 1. The asymptotic behavior near the blow-up time is also studied.展开更多
This paper deals with a heat system coupled via local and localized sources subject to null Dirichlet boundary conditions. In a previous paper of the authors, a complete result on the multiple blow-up rates was obtain...This paper deals with a heat system coupled via local and localized sources subject to null Dirichlet boundary conditions. In a previous paper of the authors, a complete result on the multiple blow-up rates was obtained. In the present paper, we continue to consider the blow-up sets to the system via a complete classification for the nonlinear parameters. That is the discussion on single point versus total blow-up of the solutions. It is mentioned that due to the influence of the localized sources, there is some substantial difficulty to be overcomed there to deal with the single point blow-up of the solutions.展开更多
This paper deals with the blow-up properties of solutions to the systems ut u(t) - Delta u = e(v(xo,t)), v(t) - Delta v = e(u(xo,t)) in Omega x (0,T) subject to either initial conditions or the initial and boundary-va...This paper deals with the blow-up properties of solutions to the systems ut u(t) - Delta u = e(v(xo,t)), v(t) - Delta v = e(u(xo,t)) in Omega x (0,T) subject to either initial conditions or the initial and boundary-value conditions. The authors show that under certain conditions the solution blows up in finite time and prove that the set of all blow-up points is the whole region. Moreover, the exact blow-up rates are also derived.展开更多
The prior estimate and decay property of positive solutions are derived for a system of quasi- linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radia...The prior estimate and decay property of positive solutions are derived for a system of quasi- linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blowup estimates for a class quasi-linear reaction-diffusion systems ( non-Newtonian filtration systems) are established, which extends the result of semi-linear reaction diffusion( Fujita type) systems.展开更多
In this article the author works with the ordinary differential equation u＂ = ｜u｜^p for some p 〉 0 and obtains some interesting phenomena concerning blow-up, blow-up rate, life-span, stability, instability, zeros ...In this article the author works with the ordinary differential equation u＂ = ｜u｜^p for some p 〉 0 and obtains some interesting phenomena concerning blow-up, blow-up rate, life-span, stability, instability, zeros and critical points of solutions to this equation.展开更多
基金supported by the National Natural Sciences Foundation of China(No.62363005)。
文摘In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial solutions with negative initial energy will blow up in finite time,and provide an upper bound estimate for the blow-up time.Additionally,we also derive a lower bound estimate for the blow-up time.
基金Supported by Shandong Provincial Natural Science Foundation(Grant Nos.ZR2021MA003 and ZR2020MA020).
文摘This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the behavior of the coefficients when time variable tends to positive infinity.Moreover,the global existence of solutions are discussed for non-positive exponents.
基金Supported by National Natural Science Foundation of China(Grant No.62363005).
文摘We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argument by contradiction with the test function techniques,we prove that not only any non-trivial solution blows up in finite time under 0<α<1,N≥1 and p>1,but also any non-trivial solution blows up in finite time underα=0,2≤N≤4 and p being the Strauss exponent.
基金supported by The Postgraduate Innovation Project of Guangzhou University(Grant No.JCCX2024-13)supported by the National Natural Science Foundation of China(Grant No.11801107).
文摘In this paper, we consider the two-dimensional incompressible Navier-Stokes-Landau-Lifshitz system. The first result is the classical Serrin-type blow-up criterion for Navier-Stokes-Landau-Lifshitz system whose index is the same as Navier-Stokes equation. More generally, we establish the blow-up criterion in the homogenous Besov space with the negative index whose form is analogue to Serrin-type. As a result, the blow-up criterion in BMO space with respect to spatial variable is also attained. These results can be regarded as the extension of the recent work [Math. Methods Appl. Sci. 46, (2023), 2500–2516].
文摘This paper deals with the blow-up properties of solutions to semilinear heat equation ut-uxx= up in (0, 1) × (0, T) with the Neumann boundary condition ux(0, t) = 0, u:x1, t) = 1 on [0, T). The necessary and sufficient conditions under which all solutions to have a finite time blow-up and the exact blow-up rates are established. It is proved that the blow-up will occur only at the boundary x = 1. The asymptotic behavior near the blow-up time is also studied.
基金China Postdoctoral Science Foundation(20110490409)Science Foundation(L2010146)of Liaoning Education Department
文摘This paper deals with a heat system coupled via local and localized sources subject to null Dirichlet boundary conditions. In a previous paper of the authors, a complete result on the multiple blow-up rates was obtained. In the present paper, we continue to consider the blow-up sets to the system via a complete classification for the nonlinear parameters. That is the discussion on single point versus total blow-up of the solutions. It is mentioned that due to the influence of the localized sources, there is some substantial difficulty to be overcomed there to deal with the single point blow-up of the solutions.
文摘This paper deals with the blow-up properties of solutions to the systems ut u(t) - Delta u = e(v(xo,t)), v(t) - Delta v = e(u(xo,t)) in Omega x (0,T) subject to either initial conditions or the initial and boundary-value conditions. The authors show that under certain conditions the solution blows up in finite time and prove that the set of all blow-up points is the whole region. Moreover, the exact blow-up rates are also derived.
文摘The prior estimate and decay property of positive solutions are derived for a system of quasi- linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blowup estimates for a class quasi-linear reaction-diffusion systems ( non-Newtonian filtration systems) are established, which extends the result of semi-linear reaction diffusion( Fujita type) systems.
文摘In this article the author works with the ordinary differential equation u＂ = ｜u｜^p for some p 〉 0 and obtains some interesting phenomena concerning blow-up, blow-up rate, life-span, stability, instability, zeros and critical points of solutions to this equation.
