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1.
《Mathematical Methods in the Applied Sciences》2018,41(2):705-713
This paper deals with the blow‐up solution to the following semilinear pseudo‐parabolic equation in a bounded domain , which was studied by Luo (Math Method Appl Sci 38(12):2636‐2641, 2015) with the following assumptions on p: and the lifespan for the initial energy J(u0)<0 is considered. This paper generalizes the above results on the following two aspects:
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2.
《Mathematical Methods in the Applied Sciences》2018,41(2):490-494
This paper deals with the blow‐up phenomena for a class of fourth‐order nonlinear wave equations with a viscous damping term with Ω = (0,1) and α > 0. Here, f(s) is a given nonlinear smooth function. For 0 < α < p – 1, we prove that the blow‐up occurs in finite time for arbitrary positive initial energy and suitable initial data. This result extends the recent results obtained by Xu et al. (Applicable Analysis)(2013) and Chen and Lu (J. Math. Anal. Appl.)(2009). Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
3.
In this work, we consider an initial boundary value problem related to the quasilinear parabolic equation for m ≥ 2,p ≥ 2, A(t) a bounded and positive definite matrix, and g a continuously differentiable decaying function, and prove, under suitable conditions on g and p, a general decay of the energy function for the global solution and a blow‐up result for the solution with both positive and negative initial energy. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
4.
《Mathematical Methods in the Applied Sciences》2018,41(5):1809-1824
In this paper, we study the zero‐flux chemotaxis‐system where Ω is a bounded and smooth domain of , n≥1, and where , k,μ>0 and α≤1. For any v≥0, the chemotactic sensitivity function is assumed to behave as the prototype χ(v)=χ0/(1+av)2, with a≥0 and χ0>0. We prove that for any nonnegative and sufficiently regular initial data u(x,0), the corresponding initial‐boundary value problem admits a unique global bounded classical solution if α<1; indeed, for α=1, the same conclusion is obtained provided μ is large enough. Finally, we illustrate the range of dynamics present within the chemotaxis system in 1, 2, and 3 dimensions by means of numerical simulations. 相似文献
5.
《Mathematical Methods in the Applied Sciences》2018,41(4):1683-1696
This paper is devoted to the study of the blow‐up phenomena of following nonlinear reaction diffusion equations with Robin boundary conditions: Here, is a bounded convex domain with smooth boundary. With the aid of a differential inequality technique and maximum principles, we establish a blow‐up or non–blow‐up criterion under some appropriate assumptions on the functions f,g,ρ,k, and u0. Moreover, we dedicate an upper bound and a lower bound for the blow‐up time when blowup occurs. 相似文献
6.
Existence and uniqueness of solutions of sequential nonlinear fractional difference equations with three‐point fractional sum boundary conditions 下载免费PDF全文
Thanin Sitthiwirattham 《Mathematical Methods in the Applied Sciences》2015,38(13):2809-2815
In this paper, we consider a discrete fractional boundary value problem of the form: where 0 < α,β≤1, 1 < α + β≤2, λ and ρ are constants, γ > 0, , is a continuous function, and Eβx(t) = x(t + β ? 1). The existence and uniqueness of solutions are proved by using Banach's fixed point theorem. An illustrative example is also presented. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
7.
This paper is concerned with the initial‐boundary value problem for one‐dimensional strongly damped wave equation involving p‐Laplacian. For p > 2 , we establish the existence of weak local attractors for this problem in . Under restriction 2 < p < 4, we prove that the semigroup, generated by the considered problem, possesses a strong global attractor in , and this attractor is a bounded subset of . Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
8.
Well‐posedness and approximation of solutions of linear divergence‐form elliptic problems on exterior regions 下载免费PDF全文
This paper describes well‐posedness, spectral representations, and approximations of solutions of uniformly elliptic, second‐order, divergence form elliptic boundary value problems on exterior regions U in when N ≥ 3. Inhomogeneous Dirichlet, Neumann, and Robin boundary conditions are treated. These problems are first shown to be well‐posed in the space E1(U) of finite‐energy functions on U using variational methods. Spectral representations of these solutions involving Steklov eigenfunctions and solutions subject to zero Dirichlet boundary conditions are described. Some approximation results for the A‐harmonic components are obtained. Positivity and comparison results for these solutions are given. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
9.
Jia Baoguo 《Mathematical Methods in the Applied Sciences》2016,39(18):5355-5364
Consider the following ν‐th order Caputo delta fractional equation (0.1) The following asymptotic results are obtained. Theorem A. Assume 0 < ν < 1 and there exists a constant b2 such that c(t)≥b2>0. Then the solutions of the equation (0.1) with x(a) > 0 satisfy 相似文献
10.
Let be the class of functions which are analytic in the unit disk . Let C(r) be the closed curve that is the image of the circle |z|=r < 1 under the mapping w = f(z), L(r) the length of C(r), and let A(r) be the area enclosed by the curve C(r). In 1968 D. K. Thomas shown that if , f is starlike with respect to the origin, and for 0≤r < 1, A(r) < A, an absolute constant, then Later, in 1969 Nunokawa has shown that if f is convex univalent, then This paper is devoted to obtaining a related correspondence between f(z) and L(r) for the case when f is univalent. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
11.
《Mathematical Methods in the Applied Sciences》2018,41(8):3018-3043
In this paper, we study the existence and concentration behavior of positive solutions for the following Kirchhoff type equation: where ɛ is a positive parameter, a and b are positive constants, and 3<p<5. Let denotes the ground energy function associated with , , where is regard as a parameter. Suppose that the potential V(x) decays to zero at infinity like |x|−α with 0<α≤2, we prove the existence of positive solutions uɛ belonging to for vanishing or unbounded K(x) when ɛ > 0 small. Furthermore, we show that the solution uɛ concentrates at the minimum points of as ɛ→0+. 相似文献
12.
Monica Marras Stella Vernier‐Piro Giuseppe Viglialoro 《Mathematical Methods in the Applied Sciences》2016,39(11):2787-2798
This paper deals with a parabolic–parabolic Keller–Segel‐type system in a bounded domain of , {N = 2;3}, under different boundary conditions, with time‐dependent coefficients and a positive source term. The solutions may blow up in finite time t?; and under appropriate assumptions on data, explicit lower bounds for blow‐up time are obtained when blow up occurs. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
13.
《Mathematical Methods in the Applied Sciences》2018,41(5):1831-1844
We consider a quantum particle in a potential V(x) subject to a time‐dependent (and spatially homogeneous) electric field E(t) (the control). Boscain, Caponigro, Chambrion, and Sigalotti proved that, under generic assumptions on V, this system is approximately controllable on the unit sphere, in sufficiently large time T. In the present article, we show that, for a large class of initial states (dense in unit sphere), approximate controllability does not hold in arbitrarily small time. This generalizes our previous result for Gaussian initial conditions. Furthermore, we prove that the minimal time can in fact be arbitrarily large. 相似文献
14.
This paper is concerned with a compressible viscoelastic fluids of Oldroyd‐B type. We prove the existence of unique local strong solutions for all initial data satisfying some compatibility condition. Moreover, we establish a blow‐up criterion for the strong solution in terms of the norm of the density tensor ρ and the norm of the symmetric tensor of constraints τ. All the results hold for the initial density vanishing from below. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
15.
Zhongyuan Liu 《Mathematical Methods in the Applied Sciences》2016,39(12):3461-3477
In this paper, we study the following biharmonic equation where , K(1) > 0,K′(1) > 0, B1(0) is the unit ball in (N≥6). We show that the aforementioned problem has infinitely many peak solutions, whose energy can be made arbitrarily large. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
16.
《Mathematical Methods in the Applied Sciences》2018,41(13):5050-5064
In this paper, we consider the following fractional Schrödinger‐Poisson system where 0 < t ≤ α < 1, , and 4α+2t ≥3 and the functions V(x), K(x) and f(x) have finite limits as |x|→∞. By imposing some suitable conditions on the decay rate of the functions, we prove that the above system has two nontrivial solutions. One of them is positive and the other one is sign‐changing. Recent results from the literature are generally improved and extended. 相似文献
17.
Boundedness in a higher‐dimensional chemotaxis system with porous medium diffusion and general sensitivity 下载免费PDF全文
Yilong Wang Xuande Zhang Qingxia Zhang 《Mathematical Methods in the Applied Sciences》2017,40(13):4758-4770
This paper deals with the following chemotaxis system: in a bounded domain with smooth boundary under no‐flux boundary conditions, where satisfies for all with l ?2 and some nondecreasing function on [0,∞ ). Here, f (v )∈C 1([0,∞ )) is nonnegative for all v ?0. It is proved that when , the system possesses at least one global bounded weak solution for any sufficiently smooth nonnegative initial data. This extends a recent result by Wang (Math. Methods Appl. Sci. 2016 39 : 1159–1175) which shows global existence and boundedness of weak solutions under the condition . Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
18.
In this article, we consider the initial boundary value problem for a class of nonlinear pseudo‐parabolic equations with a memory term: Under suitable assumptions, we obtain the local and global existence of the solution by Galerkin method. We prove finite‐time blow‐up of the solution for initial data at arbitrary energy level and obtain upper bounds for blow‐up time by using the concavity method. In addition, by means of differential inequality technique, we obtain a lower bound for blow‐up time of the solution if blow‐up occurs. 相似文献
19.
Disappearance and global existence of interfaces for a doubly degenerate parabolic equation with variable coefficient 下载免费PDF全文
Nan Li Liangchen Wang Chunlai Mu Pan Zheng 《Mathematical Methods in the Applied Sciences》2015,38(8):1465-1471
This paper deals with the Cauchy problem for a doubly degenerate parabolic equation with variable coefficient For the case λ + 1 ≥ N, one proves that depending on the behavior of the variable coefficient at infinity, the Cauchy problem either possesses the property of finite speed of propagation of perturbation or the support blows up in finite time. This completes a result by Tedeev (A.F.Tedeev, The interface blow‐up phenomenon and local estimates for doubly degenerate parabolic equations, Appl. Anal. 86 (2007) 755–782.), which asserts the same result under the condition λ + 1 < N. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
20.
Qiaoshun Yang Baoguo Jia Zhiting Xu 《Mathematical Methods in the Applied Sciences》2016,39(2):202-213
In this paper, we consider the nonlinear oscillation of the following second‐order neutral delay dynamic equations with distributed delay on a time scale , where Z(t) = x(t) + p(t)x(τ(t)),α,β > 0 are constants. By using some new techniques, we obtain oscillation criteria for the equation when β > α,β = α, and β < α, respectively. Those results established here complete and develop the oscillation criteria in the literature. Also, our main results are illustrated with some examples. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献