共查询到20条相似文献，搜索用时 15 毫秒
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QunFei Long 《偏微分方程(英文版)》2020,33(3):222-234
We investigate the initial boundary value problem of the pseudo-parabolic equation $u_{t} - triangle u_{t} - triangle u = phi_{u}u + |u|^{p - 1}u,$ where $phi_{u}$ is the Newtonian potential, which was studied by Zhu et al. (Appl. Math. Comput., 329 (2018) 38-51), and the global existence and the finite time blow-up of the solutions were studied by the potential well method under the subcritical and critical initial energy levels. We in this note determine the upper and lower bounds for the blow-up time. While estimating the upper bound of blow-up time, we also find a sufficient condition of the solution blowing-up in finite time at arbitrary initial energy level. Moreover, we also refine the upper bounds for the blow-up time under the negative initial energy. 相似文献
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This paper considers the Cauchy problem of pseudo-parabolic equation withinhomogeneous terms $u_t = ∆u+k∆u_t+w(x)u^p(x,t).$ In [1], Li et al. gave the criticalFujita exponent, second critical exponent and the life span for blow-up solutions under $w(x) = |x|^σ$ with $σ >0.$ We further generalize the weight function $w(x) ∼ |x|^σ$ for $−2<σ<0,$ and discuss the global and non-global solutions to obtain the critical Fujitaexponent. 相似文献
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On the global existence of solution to one-dimensional fourth order nonlinear Sobolev type equations
We prove the global existence and uniqueness of a classical solution to initial boundary value problem for a class of Sobolev type equations under the Dirichlet boundary conditions. This class of evolution equations covers the well-known viscous Cahn-Hilliard equation and the viscous Camassa-Holm equation. 相似文献
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The paper studies the existence,the exponential decay and the nonexistence of global solution for a class of quasilinear parabolic equations. 相似文献
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This paper investigates the properties of solutions to a quasilinear parabolicsystem with nonlocal boundary conditions and localized sources. Conditions for theexistence of global or blow-up solutions are given. Global blow-up property and blow-up rate estimates are also derived. 相似文献
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This paper deals with the initial boundary value problem for strongly damped semilinear wave equations with logarithmic nonlinearity in a bounded domain . We discuss the existence, uniqueness and polynomial or exponential energy decay estimates of global weak solutions under some appropriate conditions. Moreover, we derive the finite time blow up results of weak solutions, and give the lower and upper bounds for blow-up time by the combination of the concavity method, perturbation energy method and differential–integral inequality technique. 相似文献
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Tran-Vu Ngo;Bao-Dung Dao;Mirelson M. Freitas; 《Mathematische Nachrichten》2024,297(1):378-413
In this paper, we consider the initial boundary value problem of the generalized pseudo-parabolic equation containing viscoelastic terms and associated with Robin conditions. We establish first the local existence of solutions by the standard Galerkin method. Then, we prove blow-up results for solutions when the initial energy is negative or nonnegative but small enough or positive arbitrary high initial energy, respectively. We also establish the lifespan and the blow-up rate for the weak solution by finding the upper bound and the lower bound for the blow-up times and the upper bound and the lower bound for the blow-up rate. For negative energy, we introduce a new method to prove blow-up results with a sharper estimate for the upper bound for the blow-up times. Finally, we prove both the global existence of the solution and the general decay of the energy functions under some restrictions on the initial data. 相似文献
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This paper investigates the properties of solutions to a quasilinear parabolic system with nonlocal boundary conditions and localized sources. Conditions for the existence of global or blow-up solutions are given. Global blow-up property and blow- up rate estimates are also derived. 相似文献
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This paper is concerned with the semilinear heat equation u_t = Δu - u^{-q} in Ω × (0, T) under the nonlinear boundary condition frac{∂u}{∂v} = u^p on ∂Ω × (0, T). Criteria for finite time quenching and blow-up are established, quenching and blow-up sets are discussed, and the rates of quenching and blow-up are obtained. 相似文献
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This paper deals with the blow-up properties of positive solutions to a localized degenerate and singular parabolic equation with weighted nonlocal boundary condi- tions. Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. Furthermore, the global blow-up behavior and the uniform blow-up profile of blow-up solutions are also described. We find that the blow-up set is the whole domain {0, a}, including the boundaries, and this differs from parabolic equations with local sources case or with homogeneous Dirichlet boundary conditions case. 相似文献
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Global Existence and Blow-up of Solutions to Multi-dimensional （n ≤ 5） Viscous Cahn-Hilliard Equation 总被引：1，自引：0，他引：1
In this paper we consider the viscous Cahn-Hilliard equation with spatial dimension n ≤5, and established global existence of weak solutions for small initial value and blow-up of solutions for any nontrivial initial data. 相似文献
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该文研究具有多项式非线性项和粘性项的非线性抛物方程的初边值问题.在一定条件下,我们得到方程的弱解全局存在.在另一些条件下,我们得到该方程的解将在有限时刻爆破,并给出了爆破时间的上界,该上界受初始函数及其支集控制.该结论推广了Messaoudi在文献[15,16]中的工作. 相似文献
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Hui-ling LI & Ming-xin WANG Department of Mathematics Southeast University Nanjing China 《中国科学A辑(英文版)》2007,50(4):590-608
This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vazquez and the comparison principle, we deduce that the blow-up occurs only on the boundary (?)Ω. In addition, for a bounded Lipschitz domainΩ, we establish the blow-up rate estimates for the positive solution to this problem with a= 0. 相似文献
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Xiatong Li;Zhong Bo Fang; 《Mathematische Nachrichten》2024,297(6):2148-2174
This paper deals with the infinite blow-up phenomena for a class of damped plate equations with logarithmic nonlinearity under the Navier boundary condition. Combining potential well method and modified differential inequality technique, we establish the infinite blow-up result of solutions with arbitrary initial energy. In particular, it is not necessary to suppose that the initial velocity and the initial displacement should have the same sign in the sense of the L2${L^2}$ inner product, that is, the solution may blow up at infinity even ∫Ωu0u1dx<0$int _Omega {{u_0}{u_1}dx} < 0$, more precisely, . 相似文献
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Yaojun Ye 《Applicable analysis》2017,96(16):2869-2890
The initial-boundary value problem for a system of Petrovsky equations with memory and nonlinear source terms in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set, and obtain the exponential decay estimate of global solutions. Meanwhile, under suitable conditions on relaxation functions and the positive initial energy as well as non-positive initial energy, it is proved that the solutions blow up in the finite time and the lifespan estimates of solutions are also given. 相似文献