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Abstract: Abstract In this paper we consider autonomous thermoelastic plate systems with Neumann boundary conditions when some reaction terms are concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary as a parameter \(\varepsilon\) goes to zero. We present some remarks on asymptotic behavior of the global attractors which lead us to conclude the lower semicontinuity of this attractors at \(\varepsilon\) equal to zero. We also prove the finite-dimensionality of the attractors. PubDate: 2022-10-30

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Abstract: Abstract This work is concerned with necessary and sufficient conditions for oscillation of all solutions of 2-dim first order neutral delay difference system with constant coefficient of the form: $$ \Delta \left[ \begin{array}{c} x(n)-px(n-m)\\ y(n)-py(n-m) \\ \end{array} \right] = \left[ \begin{array}{cc} a & b \\ c & d \\ \end{array} \right] \left[ \begin{array}{c} x(n-\alpha )\\ y(n-\beta )\\ \end{array} \right] , n\ge n_{0} $$ by constructing several suitable characteristic equations. Also, an effort has been made to apply some results to nonlinear neutral systems aheading linearized oscillation theory. Some examples are in the discussion to illustrate our results. PubDate: 2022-10-15

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Abstract: Abstract This paper studies a pursuit differential game in a closed convex subset of the Euclidean space \({\mathbb {R}}^n.\) Players of the game consist of finite number of pursuers chasing to catch a single evader both of which moves according to certain first order differential equation. The differential equations involve control functions through which players make their inputs in the game. Each of the player’s control function is subject to the coordinate-wise integral constraint. Pursuers are deemed to catch the evader when the geometric position of at least one pursuer coincides with that of the evader. We describe strategies of the pursuers in phases and give formula for computing the time span of each phase. Moreover, we provide and conditions that ensure evader’s catch. PubDate: 2022-10-15

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Abstract: Abstract In this paper, we consider the initial value problem for a \(2 \times 2\) system of non-strictly hyperbolic conservation laws. The first equation is a convex conservation law whose flux has linear growth at infinity and has an asymptotic limit under a scaling. The second equation is linear and exhibits measure-valued solution even if the initial data is smooth with compact support. We use a scaling argument to derive explicit formula of solution for the system with the asymptotic flux function where the second equation becomes linear with discontinuous coefficient. We also study properties of solution when the initial data is periodic with zero mean over the period. Our theory is illustrated using the Lax equation. PubDate: 2022-10-13

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Abstract: Abstract Using Mountain Pass Theorem, we consider the existence of weak solutions of weighted Robin problem involving \(p\left( .\right)\) -biharmonic operator $$\begin{aligned} \left\{ \begin{array}{cc} a\left( x\right) \Delta _{p\left( x\right) }^{2}u=\lambda b(x)\left u\right ^{q(x)-2}u, &{} in~\Omega \\ a(x)\left \Delta u\right ^{p(x)-2}\frac{\partial u}{\partial \upsilon }+\beta (x)\left u\right ^{p(x)-2}u=0, &{} on~\partial \Omega \end{array} \right. \end{aligned}$$ under some conditions in the space \(W_{a,b}^{2,p(.)}\left( \Omega \right) .\) PubDate: 2022-10-10

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Abstract: Abstract This paper introduces a realistic framework for the blood flow dynamics in the human circulatory system, wherein blood changes its characteristics while flowing through different arteries, from elastic to muscular to rigid. We believe that this approach is significantly different from most of the literature of the related work, wherein the blood flow characteristics remain the same throughout its flow in an artery. Another interesting idea in this work is the introduction of a nonlinear relationship between flux and the pressure gradient that has been found appropriate for the blood flow in coronary arteries. Further, this work suggests to the researchers that if one considers the varying material properties of the blood that flows through the different constituent pipes (blood vessels), one would be able to gain adequate understanding on the vital issues in treating the problems related to blood circulation, such as blood clots, stenotic growth and bypass grafting surgeries. PubDate: 2022-10-05

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Abstract: Abstract By using variational methods and critical point theory, we obtain criteria for the existence of at least three solutions for a generalized fourth order nonlinear difference equation together with periodic boundary conditions. Various special cases of the above problem are discussed. An example is included to illustrate the results. PubDate: 2022-10-01

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Abstract: Abstract In this paper, a bi-dimensional continuous-time stochastic differential system of Leslie–Grower types is considered. The proposed predator-prey model with white noises is theoretically and numerically investigated. The global existence of the positive unique solution of the model is obtained. The boundedness in the sense of moments of the solution is shown. Some asymptotic properties of the stochastic system are also elaborated. New methodological approaches based on the statistical linearisation method as well as on the coupled and weighted procedures are elaborated. Numerical results of the density function for the stationary state are obtained. PubDate: 2022-10-01

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Abstract: Abstract We consider a nonlocal boundary value problem for a feedback control system governed by a fractional degenerate (Sobolev type) semilinear differential inclusion in a Banach space. To solve this problem, we introduce a multivalued integral operator whose fixed points determine its solutions and study the properties of this operator. It is demonstrated, in particular, that the operator is condensing with respect to an appropriate measure of noncompactness in a functional space. This makes it possible to formulate a general existence principle (Theorem 33) in terms of the topological degree theory. Theorem 34 gives an example of a concrete realization of this principle. As its corollary we get the existence of an optimal solution to our problem (Theorem 35). Some important particular cases including a nonlocal Cauchy problem, periodic and anti-periodic boundary value problems are presented. As example, we consider the existence of an optimal periodic solution for a fractional diffusion type degenerate control system. PubDate: 2022-10-01

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Abstract: Abstract In this paper, we prove the existence and uniqueness of a non-negative monotonically increasing solution of the boundary value problem (BVP) $$\begin{aligned}&H''(\eta )-H^p(\eta )H'(\eta )+\frac{\eta }{2}H'(\eta )+\frac{1}{2p}H(\eta )=0,\quad \eta >0,\\&H(0)=0,\quad \lim _{\eta \rightarrow +\infty }\eta ^{-\frac{1}{p}}H(\eta )=1, \end{aligned}$$ using a shooting argument for \(p>1\) . This BVP arises when we construct the large time asymptotic solution of the modified Burgers equation, using the method of matched asymptotic expansions, on the quarter plane. PubDate: 2022-10-01

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Abstract: Abstract Fermi–Walker derivative and energy of curves play an important role in sensible guidelines. In this study we formulate a new energy for Fermi–Walker (FW) derivative of normal spherical image by using FW parallelism in Lie groups. By means of innovative illustration, we get new necessary and sufficient condition for the given field to be FW parallel. We give some partial differential equations. Moreover, we have some energy construction for normal spherical image in Lie groups. PubDate: 2022-10-01

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Abstract: Abstract This paper is concerned with obtaining the approximate numerical solution of two-dimensional linear stochastic Volterra integral equation by using two-dimensional Bernstein polynomials as basis. Properties of these polynomials and operational matrix of integration together with the product operational matrix are utilized to transform the integral equation to a matrix equation which corresponds to a system of linear algebraic equations with unknown Bernstein coefficients. Some theorems are included to show the convergence and advantage of the proposed method. The numerical example illustrates the efficiency and accuracy of the method. PubDate: 2022-10-01

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Abstract: Abstract This paper is concerned with an infinite horizon optimal control with unbounded value functions for a class of Hamilton–Jacobi equations (HJEs) in Banach spaces. Based on the uniqueness of \(\beta \) -viscosity solutions of HJEs, which is first established in this paper, necessary and sufficient optimality conditions are derived. PubDate: 2022-10-01

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Abstract: Abstract The paper is concerned with the extension of a monotone iterative technique to impulsive finite delay differential equations of fractional order with a nonlocal initial condition in an ordered Banach space. We study the existence of extremal mild solutions with or without assuming the compactness of a semigroup and also prove the uniqueness of the mild solution of the system. The results are obtained with the help of fractional calculus, a measure of non-compactness, the semigroup theory and monotone iterative technique. Finally, an example is provided to show the application of our main. PubDate: 2022-10-01

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Abstract: Abstract This paper studies the limit cycles produced by small perturbations of certain planar Hamiltonian systems. The limit cycles under consideration correspond to critical levels of the Hamiltonian, that is they are located in a small vicinity of a separatrix contour or a critical point. Two most interesting facts in the paper are that the Hamiltonian function is not a polynomial and that the system under consideration comes from a model of oscillator with a pair of irrational nonlinearities, which implies the transition from smooth to discontinuous dynamics. This model has been proposed recently by Han et al. in a paper published in 2012. PubDate: 2022-10-01

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Abstract: Abstract In this paper we prove the existence of mild solutions for a second-order impulsive semilinear stochastic differential inclusion with an infinite-dimensional standard cylindrical Wiener process and Poisson jumps. We consider non convex-valued cases. PubDate: 2022-10-01

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Abstract: Abstract In this article, we consider a nonlinear Sobolev type fractional functional integrodifferential equations in a Banach space along with a nonlocal condition. Sufficient conditions for existence, uniqueness and dependence on initial data of local solutions of considered problem are derived by employing fixed point techniques and theory of classical semigroup. Further, we also render the criteria for existence of global solution. At the end, we provide an application to elaborate the obtained results. PubDate: 2022-10-01

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Abstract: Abstract In this paper, a numerical technique is proposed to solve a two-dimensional coupled Burgers’ equation. The two-dimensional Cole–Hopf transformation is applied to convert the nonlinear coupled Burgers’ equation into a two-dimensional linear diffusion equation with Neumann boundary conditions. The diffusion equation with Neumann boundary conditions is semi-discretized using MOL in both x and y directions. This process yielded the system of ordinary differential equations in the time variable. Multistep methods namely backward differentiation formulas of order one, two and three are employed to solve the ode system. Efficiency and accuracy of the proposed methods are verified through numerical experiments. The proposed schemes are simple, accurate, efficient and easy to implement. PubDate: 2022-10-01

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Abstract: Abstract In this paper, we propose a method of successive approximations for nonlinear fuzzy Fredholm integral equations of the second kind. The main approximation tool is based on fuzzy block-pulse functions. The error estimation of the proposed method is established. A number of illustrative examples that demonstrate accuracy and convergence is given as well. PubDate: 2022-10-01

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Abstract: Abstract This article examines a compact scheme employing fuzzy transform via exponential basis to solve nonlinear stationary convection–diffusion equations. The scheme executes approximated fuzzy components which estimate the solution values with fourth-order accuracy in an optimal computing time. Such an arrangement associates the approximated fuzzy components with solution values by a linear system. The Jacobian matrices in the scheme are monotone and irreducible. The proof of convergence is briefly discussed. Numerical simulations with nonlinear and linear convection–diffusion equations occurring in quantum mechanics and rheological Carreau fluid will be examined to corroborate the new scheme's utility and efficiency of computational convergence order. PubDate: 2022-10-01