共查询到20条相似文献,搜索用时 31 毫秒
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This paper deals with a two-competition-species chemotaxis-Navier-Stokes system with two different consumed signals in a smooth bounded domain under zero Neumann boundary conditions for , and homogeneous Dirichlet boundary condition for , where the parameters ( ) and ( ) are positive. This system describes the evolution of two-competing species which react on two different chemical signals in a liquid surrounding environment. Recently, the boundedness and stabilization of classical solutions to the above system under two-dimensional case have been derived in the previous works. However, to the best of our knowledge, the well-posedness problem of solutions for the above system is still open in the three dimensional setting, because of the difficulties in the Navier-Stokes system. The aim of this paper is to construct global weak solutions and show that after some waiting time, these weak solutions become eventually smooth. 相似文献
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In this article, we study the blow‐up of the damped wave equation in the scale‐invariant case and in the presence of two nonlinearities. More precisely, we consider the following equation: with small initial data. For and μ ∈ (0, μ?) , where μ? > 0 is depending on the nonlinearties' powers and the space dimension (μ? satisfies ), we prove that the wave equation, in this case, behaves like the one without dissipation (μ = 0 ). Our result completes the previous studies in the case where the dissipation is given by , where, contrary to what we obtain in the present work, the effect of the damping is not significant in the dynamics. Interestingly, in our case, the influence of the damping term is important. 相似文献
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We provide a characterization for the existence and uniqueness of solutions in the space of vector‐valued sequences for the multiterm fractional delayed model in the form where X is a Banach space, A is a closed linear operator with domain D(A) defined on X, and ΔΓ denotes the Grünwald–Letkinov fractional derivative of order Γ > 0. We also give some conditions to ensure the existence of solutions when adding nonlinearities. Finally, we illustrate our results with an example given by a general abstract nonlinear model that includes the fractional Fisher equation with delay. 相似文献
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This paper deals with the following slightly subcritical Schrödinger equation: where is a nonnegative smooth function, , , , . Most of the previous works for the Schrödinger equations were mainly investigated for power-type nonlinearity. In this paper, we will study the case when the nonlinearity is a non-power nonlinearity. We show that, for ε small enough, there exists a family of single-peak solutions concentrating at the positive stable critical point of the potential . 相似文献
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Rong Yin Jihui Zhang Xudong Shang 《Mathematical Methods in the Applied Sciences》2020,43(15):8736-8752
This paper is dedicated to studying the following Schrödinger–Poisson system Under some different assumptions on functions V(x), K(x), a(x) and f(u), by using the variational approach, we establish the existence of positive ground state solutions. 相似文献
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In this paper, we study the existence of ground state solutions for the modified fractional Schrödinger equations where , , , and are positive parameters, , denotes the fractional Laplacian of order . For the case and the case , the existence results of ground state solutions are given, respectively. 相似文献
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In this paper, we study the following Schrödinger-Poisson equations: where , is a parameter and and satisfy the critical frequency conditions. By using variational methods and penalization arguments, we show the existence of multibump solutions for the above system. Furthermore, the heights of these bumps are different order. 相似文献
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Stevo Stevi 《Mathematical Methods in the Applied Sciences》2022,45(1):546-556
We investigate the following multilinear integral operator where and is a continuous kernel function satisfying the condition for some functions , which are continuous, increasing, , and a function , from a product of weighted-type spaces to weighted-type spaces of real functions. We calculate the norm of the operator, extending and complementing some results in the literature. We also give an explanation for a relation between integrals of an Lp integrable function and its radialization on . 相似文献
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In this paper, we concern with the following fractional p‐Laplacian equation with critical Sobolev exponent where ε > 0 is a small parameter, λ > 0 , N is a positive integer, and N > ps with s ∈ (0, 1) fixed, . Since the nonlinearity does not satisfy the following Ambrosetti‐Rabinowitz condition: with μ > p , it is difficult to obtain the boundedness of Palais‐Smale sequence, which is important to prove the existence of positive solutions. In order to overcome the above difficulty, we introduce a penalization method of fractional p‐Laplacian type. 相似文献
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Jia‐Feng Liao 《Mathematical Methods in the Applied Sciences》2021,44(1):407-418
In this article, we devote ourselves to investigate the following singular Kirchhoff‐type equation: where is a bounded domain with smooth boundary ?Ω,0∈Ω,a≥0,b,λ>0,0<γ,s<1, and By using the variational and perturbation methods, we obtain the existence of two positive solutions, which generalizes and improves the recent results in the literature. 相似文献
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This article examines the existence and uniqueness of weak solutions to the d‐dimensional micropolar equations (d=2 or d=3) with general fractional dissipation (?Δ)αu and (?Δ)βw. The micropolar equations with standard Laplacian dissipation model fluids with microstructure. The generalization to include fractional dissipation allows simultaneous study of a family of equations and is relevant in some physical circumstances. We establish that, when and , any initial data (u0,w0) in the critical Besov space and yields a unique weak solution. For α ≥ 1 and β=0, any initial data and also leads to a unique weak solution as well. The regularity indices in these Besov spaces appear to be optimal and can not be lowered in order to achieve the uniqueness. Especially, the 2D micropolar equations with the standard Laplacian dissipation, namely, α=β=1, have a unique weak solution for . The proof involves the construction of successive approximation sequences and extensive a priori estimates in Besov space settings. 相似文献
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Jiabin Zuo Tianqing An Alessio Fiscella 《Mathematical Methods in the Applied Sciences》2021,44(1):1071-1085
The paper deals with the following Kirchhoff‐type problem where M models a Kirchhoff coefficient, is a variable s(·) ‐order p(·) ‐fractional Laplace operator, with and . Here, is a bounded smooth domain with N > p(x, y)s(x, y) for any , μ is a positive parameter, g is a continuous and subcritical function, while variable exponent r(x) could be close to the critical exponent , given with and for . We prove the existence and asymptotic behavior of at least one non‐trivial solution. For this, we exploit a suitable tricky step analysis of the critical mountain pass level, combined with a Brézis and Lieb‐type lemma for fractional Sobolev spaces with variable order and variable exponent. 相似文献
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Anton A. Lunyov 《Mathematische Nachrichten》2023,296(9):4125-4151
The paper is concerned with the Bari basis property of a boundary value problem associated in with the following 2 × 2 Dirac-type equation for : with a potential matrix and subject to the strictly regular boundary conditions . If , this equation is equivalent to one-dimensional Dirac equation. We show that the normalized system of root vectors of the operator is a Bari basis in if and only if the unperturbed operator is self-adjoint. We also give explicit conditions for this in terms of coefficients in the boundary conditions. The Bari basis criterion is a consequence of our more general result: Let , , boundary conditions be strictly regular, and let be the sequence biorthogonal to the normalized system of root vectors of the operator . Then, These abstract results are applied to noncanonical initial-boundary value problem for a damped string equation. 相似文献
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Damián Pinasco 《Mathematische Nachrichten》2023,296(8):3593-3605
We prove that given any set of n unit vectors , the inequality holds for . Moreover, the equality is attained if and only if is an orthonormal system. 相似文献
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Nguyen Anh Triet Le Thi Phuong Ngoc Alain Pham Ngoc Dinh Nguyen Thanh Long 《Mathematical Methods in the Applied Sciences》2021,44(1):668-692
This paper is devoted to the study of a nonlinear wave equation with initial conditions and nonlocal boundary conditions of 2N‐point type, which connect the values of an unknown function u(x,t) at x = 1, x = 0, x = ηi(t) , and x = θi(t), where for all t ≥ 0. First, we prove local existence of a unique weak solution by using density arguments and applying the Banach's contraction principle. Next, under the suitable conditions, we show that the problem considered has a unique global solution u(t) with energy decaying exponentially as t → +∞ . Finally, we present numerical results. 相似文献
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For and variable exponents and with values in [1, ∞], let the variable exponents be defined by The Riesz–Thorin–type interpolation theorem for variable Lebesgue spaces says that if a linear operator T acts boundedly from the variable Lebesgue space to the variable Lebesgue space for , then where C is an interpolation constant independent of T. We consider two different modulars and generating variable Lebesgue spaces and give upper estimates for the corresponding interpolation constants Cmax and Csum, which imply that and , as well as, lead to sufficient conditions for and . We also construct an example showing that, in many cases, our upper estimates are sharp and the interpolation constant is greater than one, even if one requires that , are Lipschitz continuous and bounded away from one and infinity (in this case, ). 相似文献
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Oleksandr V. Hadzhy Igor I. Skrypnik Mykhailo V. Voitovych 《Mathematische Nachrichten》2023,296(9):3892-3914
We prove continuity and Harnack's inequality for bounded solutions to elliptic equations of the type under the precise choice of μ. 相似文献
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This is the second of a series of two papers that studies the fractional porous medium equation, with and , posed on a Riemannian manifold with isolated conical singularities. The first aim of the article is to derive some useful properties for the Mellin–Sobolev spaces including the Rellich–Kondrachov theorem and Sobolev–Poincaré, Nash and Super Poincaré type inequalities. The second part of the article is devoted to the study the Markovian extensions of the conical Laplacian operator and its fractional powers. Then based on the obtained results, we establish existence and uniqueness of a global strong solution for initial data and all . We further investigate a number of properties of the solutions, including comparison principle, contraction and conservation of mass. Our approach is quite general and thus is applicable to a variety of similar problems on manifolds with more general singularities. 相似文献