Let Ω R^n be a bounded domain with a smooth boundary. We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term Based on a time-uniform priori estimate method, the existence ...Let Ω R^n be a bounded domain with a smooth boundary. We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term Based on a time-uniform priori estimate method, the existence of the compact global attractor is proved for this model in the phase space H^（^） x L2（~）.展开更多
In this paper,we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type.By using methods of an iteration argument and di erential inequalities,we obtain the blow-...In this paper,we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type.By using methods of an iteration argument and di erential inequalities,we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions.Meanwhile,we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation.展开更多
In this paper we discuss the bounds for the modulus of continuity of the blow-up time with respect to three parameters of λ, h, and p respectively for the initial boundary value problem of the semilinear parabolic eq...In this paper we discuss the bounds for the modulus of continuity of the blow-up time with respect to three parameters of λ, h, and p respectively for the initial boundary value problem of the semilinear parabolic equation.展开更多
In this paper, we study the nonexistence of solutions of the following time fractional nonlinear Schr?dinger equations with nonlinear memory where 0, ιλ denotes the principal value of ιλ, p>1, T>0, λ∈C/{0}...In this paper, we study the nonexistence of solutions of the following time fractional nonlinear Schr?dinger equations with nonlinear memory where 0, ιλ denotes the principal value of ιλ, p>1, T>0, λ∈C/{0}, u(t,x) is a complex-value function, denotes left Riemann-Liouville fractional integrals of order 1-λ and is the Caputo fractional derivative of order . We obtain that the problem admits no global weak solution when and under different conditions for initial data.展开更多
This paper addresses the existence of a global attractor for Kirchhoff-type strongly damped wave equation with nonlinear memory effects.The key innovation of our work lies in reformulating the historical memory term a...This paper addresses the existence of a global attractor for Kirchhoff-type strongly damped wave equation with nonlinear memory effects.The key innovation of our work lies in reformulating the historical memory term as a convolution integral involving the memory kernel μ and a nonlinear powerlaw function |u(s)|^(β) u(s).First,we rigorously establish the existence,uniqueness,and regularity of solutions for Equation(1.2)through a systematic application of a priori energy estimates and the Faedo-Galerkin approximation method,while simultaneously demonstrating the presence of a bounded absorbing set.To analyze the asymptotic dynamics,we decompose the solution semigroup S(t)into two components:S_(1),governed by higher-order regularity,and S_(2)( t),capturing dissipative effects.The compactness ofS_(1) is established via operator regularity analysis combined with the compact sobolev embedding theorem,while the uniform exponential decay of S_(2) is proven through refined energy estimation techniques.By synthesizing these results,we conclusively demonstrate the existence of a global attractor for the system under study,thereby extending the theoretical framework for nonlinear wave equations with memory-driven dissipation.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
The present paper is devoted to studying the initial-boundary value problem of a 1-D wave equation with a nonlinear memory: u_(tt) - u_(xx) = 1/ Γ(1 - γ) ∫_0~t (t - s)^(-γ)|u(s)|~pds. The blow up result will be es...The present paper is devoted to studying the initial-boundary value problem of a 1-D wave equation with a nonlinear memory: u_(tt) - u_(xx) = 1/ Γ(1 - γ) ∫_0~t (t - s)^(-γ)|u(s)|~pds. The blow up result will be established when p > 1 and 0 < γ < 1, no matter how small the initial data are, by introducing two test functions and a new functional.展开更多
In this paper we study the local or global(in time)existence of small data solutions to semi-linear fractionalσ-evolution equations with nonlinear memory.Our main goals is to explain on the one hand the influence of ...In this paper we study the local or global(in time)existence of small data solutions to semi-linear fractionalσ-evolution equations with nonlinear memory.Our main goals is to explain on the one hand the influence of the memory term and on the other hand the influence of higher regularity of the data on qualitative properties of solutions.展开更多
In this paper,we investigate a reaction-diffusion equation ut-duxx=au+∫t0up(x,τ)dT+k(x)with double free boundaries.We study blowup phenomena in finite time and asymptotic behavior of time-global solutions.Our result...In this paper,we investigate a reaction-diffusion equation ut-duxx=au+∫t0up(x,τ)dT+k(x)with double free boundaries.We study blowup phenomena in finite time and asymptotic behavior of time-global solutions.Our results show if∫h0-hok(x)φ1dx is large enough,then the blowup occurs.Meanwhile we also prove when T*<+oo,the solution must blow up in finite time.On the other hand,we prove that the solution decays at an exponential rate and the two free boundaries converge to a finite limit provided the initial datum is small sufficiently.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 10471018)
文摘Let Ω R^n be a bounded domain with a smooth boundary. We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term Based on a time-uniform priori estimate method, the existence of the compact global attractor is proved for this model in the phase space H^（^） x L2（~）.
基金Supported by the Natural Science Foundation of China(Grant No.11371175)Innovation Team Project in Colleges and Universities of Guangdong Province(Grant No.2020WCXTD008)+1 种基金Science Foundation of Huashang College Guangdong University of Finance&Economics(Grant No.2020HSDS01)Science Research Team Project in Guangzhou Huashang College(Grant No.2021HSKT01).
文摘In this paper,we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type.By using methods of an iteration argument and di erential inequalities,we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions.Meanwhile,we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation.
基金The NSF (10572154,60873088) of Chinathe NCET-06-0731the NSF (7004569,7003624) of Guangdong,China
文摘In this paper we discuss the bounds for the modulus of continuity of the blow-up time with respect to three parameters of λ, h, and p respectively for the initial boundary value problem of the semilinear parabolic equation.
文摘In this paper, we study the nonexistence of solutions of the following time fractional nonlinear Schr?dinger equations with nonlinear memory where 0, ιλ denotes the principal value of ιλ, p>1, T>0, λ∈C/{0}, u(t,x) is a complex-value function, denotes left Riemann-Liouville fractional integrals of order 1-λ and is the Caputo fractional derivative of order . We obtain that the problem admits no global weak solution when and under different conditions for initial data.
文摘This paper addresses the existence of a global attractor for Kirchhoff-type strongly damped wave equation with nonlinear memory effects.The key innovation of our work lies in reformulating the historical memory term as a convolution integral involving the memory kernel μ and a nonlinear powerlaw function |u(s)|^(β) u(s).First,we rigorously establish the existence,uniqueness,and regularity of solutions for Equation(1.2)through a systematic application of a priori energy estimates and the Faedo-Galerkin approximation method,while simultaneously demonstrating the presence of a bounded absorbing set.To analyze the asymptotic dynamics,we decompose the solution semigroup S(t)into two components:S_(1),governed by higher-order regularity,and S_(2)( t),capturing dissipative effects.The compactness ofS_(1) is established via operator regularity analysis combined with the compact sobolev embedding theorem,while the uniform exponential decay of S_(2) is proven through refined energy estimation techniques.By synthesizing these results,we conclusively demonstrate the existence of a global attractor for the system under study,thereby extending the theoretical framework for nonlinear wave equations with memory-driven dissipation.
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 the National Natural Sicence Foundation of China(Nos.11301489,11401367,11501273)the Natural Science Foundation of Zhejiang Province(Nos.LQ13A010013,LY14A010010)the Doctoral Fund of Ministry of Education of China(No.20133108120002)
文摘The present paper is devoted to studying the initial-boundary value problem of a 1-D wave equation with a nonlinear memory: u_(tt) - u_(xx) = 1/ Γ(1 - γ) ∫_0~t (t - s)^(-γ)|u(s)|~pds. The blow up result will be established when p > 1 and 0 < γ < 1, no matter how small the initial data are, by introducing two test functions and a new functional.
基金The research of this article is supported by the DAAD,Erasmus+Project between the Hassiba Benbouali University of Chlef(Algeria)and TU Bergakademie Freiberg,2015-1-DE01-KA107-002026
文摘In this paper we study the local or global(in time)existence of small data solutions to semi-linear fractionalσ-evolution equations with nonlinear memory.Our main goals is to explain on the one hand the influence of the memory term and on the other hand the influence of higher regularity of the data on qualitative properties of solutions.
基金Research supported by the National Natural Science Foundation of China(No.11801209)Natural Science Fund for Colleges and Universities in Jiangsu Province(No.18KJB110004)College Students'Innovation Project of Jiangsu Province(No.201810323012Z).
文摘In this paper,we investigate a reaction-diffusion equation ut-duxx=au+∫t0up(x,τ)dT+k(x)with double free boundaries.We study blowup phenomena in finite time and asymptotic behavior of time-global solutions.Our results show if∫h0-hok(x)φ1dx is large enough,then the blowup occurs.Meanwhile we also prove when T*<+oo,the solution must blow up in finite time.On the other hand,we prove that the solution decays at an exponential rate and the two free boundaries converge to a finite limit provided the initial datum is small sufficiently.
