Article
Mathematics, Applied
Nhan Cong Le, Truong Xuan Le, Y. Van Nguyen
Summary: This work focuses on a class of nonlinear viscoelastic wave equations with strong damping and variable exponent sources. Unlike previous works, this paper uses the potential well method to study both the finite time blow-up of solutions starting from unstable sets and the decay estimate for global solutions starting in potential wells.
APPLICABLE ANALYSIS
(2023)
Article
Mathematics, Applied
Muhammad Mustafa
Summary: In this paper, we investigate the interaction between two types of damping in a viscoelastic Timoshenko system. We establish explicit energy decay rates for this system, which generalize and improve upon earlier related results.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Jianghao Hao, Fangqing Du
Summary: This article investigates a viscoelastic wave equation with variable coefficients, logarithmic nonlinearity, and dynamic boundary conditions in a bounded domain. The global existence of a solution is proven using the potential well method. In the stable set, a decay rate result is established without restrictive assumptions on the relaxation function behavior at infinity, while blow-up of the solution is obtained in the unstable set.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Mohammad Shahrouzi
Summary: In this paper, a class of Lame inverse source problem with variable-exponent nonlinearities is studied. It is shown that solutions decay as time goes to infinity under certain conditions, and blow up in finite time in the absence of a damping term under other conditions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Y. Nguyen Van, Le Cong Nhan, Le Xuan Truong
Summary: In this paper, the global existence and finite time blow-up of a nonlinear thermo-viscoelastic system are studied. The exponential decay of solutions in the former case and the lower and upper bounds for blow-up time of the blow-up solutions in the latter case are proved by constructing appropriate Lyapunov functionals.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
Article
Mathematics, Applied
Ngo Tran Vua, Dao Bao Dung, Huynh Thi Hoang Dung
Summary: This paper considers the initial boundary value problem of the generalized pseudo-parabolic equation containing a viscoelastic term. The local existence of solutions is established using Banach's fixed point theorem. Blow-up results for solutions are then proven for cases of negative initial energy, nonnegative but sufficiently small initial energy, and arbitrarily high initial energy. Lifespan and blow-up rate for the weak solution are also established by finding upper and lower bounds for the blow-up times and rates. A new method with sharper estimates is introduced to prove blow-up results for negative energy. Finally, global existence of the solution and a general decay estimate are proven under suitable assumptions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Jamilu Hashim Hassan, Salim A. Messaoudi
Summary: This paper considers a viscoelastic wave equation with a general relaxation function and nonlinear frictional damping of variable-exponent type. The authors provide explicit and general decay results for the energy of the system based on the decay rate of the relaxation function and the nature of the variable-exponent nonlinearity, extending existing literature results to the case of nonlinear frictional damping of variable-exponent type.
ASYMPTOTIC ANALYSIS
(2021)
Article
Mathematics, Applied
Salim A. Messaoudi, Mohammad M. Al-Gharabli, Adel M. Al-Mahdi
Summary: This paper investigates the viscoelastic problem with variable exponent nonlinearities and relaxation functions. Such problems arise in fluid dynamics and electrorheological fluids. The authors use Lebesgue and Sobolev spaces with variable exponents to analyze the problem and prove a global existence result using the well-depth method. They also establish explicit and general decay results under a very general assumption on the relaxation function. These results extend and generalize previous findings in the literature.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Jiaqi Liu, Fengjie Li
Summary: This paper discusses a homogeneous Dirichlet initial-boundary problem of parabolic equations with different space-time coefficients and studies the Fujita exponents of solutions and the simultaneous or non-simultaneous blow-up of the two components of blow-up solutions.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Mathematics, Applied
Mohammad Shahrouzi, Jorge Ferreira, Faramarz Tahamtani
Summary: This work studies the global behavior of solutions for a system of (p(x),q(x))-Kirchhoff-type equations. The global existence of solutions is proven, and the general decay of solutions is confirmed by constructing suitable auxiliary functionals when the exponents satisfy appropriate conditions. Additionally, the finite time blow-up of solutions with negative initial energy is established under suitable conditions on data.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Mohammad M. Al-Gharabli, Adel M. Al-Mahdi, Mohammad Kafini
Summary: In this paper, a viscoelastic problem with variable exponent and logarithmic nonlinearities is considered. Global existence is proved using the well-depth method, and explicit and general decay results are established under various relaxation functions and specific conditions on the variable exponent function. These results extend and generalize many earlier findings in the literature.
Article
Mathematics, Applied
Sun-Hye Park
Summary: In this article, the study focuses on blow-up results of a strongly damped von Karman equation with variable exponent source and memory effects, with attention to solutions with varying levels of initial energy. The estimation of both upper and lower bounds of blow-up time is also conducted.
BOUNDARY VALUE PROBLEMS
(2021)
Article
Mathematics, Applied
Menglan Liao, Zhong Tan
Summary: This paper deals with the Petrovsky equation with damping and nonlinear sources, studying the upper and lower bounds of the blow-up time under different energy conditions, as well as presenting the global existence of solutions and an energy decay estimate.
SCIENCE CHINA-MATHEMATICS
(2023)
Article
Mathematics, Applied
Sun-Hye Park
Summary: In this paper, we discuss a viscoelastic von Karman equation with damping, delay, and source effects of variable exponent type. We prove the global existence of solutions using the potential well method and derive general decay results under more general conditions of a relaxation function by employing the perturbed energy method and properties of convex functions. Our results extend and complement previous studies on von Karman equations.
BOUNDARY VALUE PROBLEMS
(2022)
Article
Mathematics
Jorge Ferreira, Erhan Piskin, Mohammad Shahrouzi
Summary: In this paper, we study a plate viscoelastic p(x)-Kirchhoff type equation with variable-exponent nonlinearities. We prove the decay property of the solution energy under appropriate conditions, and show that solutions blow up in a finite time with negative initial energy and a suitable range of variable exponents.
QUAESTIONES MATHEMATICAE
(2023)
Article
Mathematics, Applied
Mohammad Shahrouzi
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2016)
Article
Mathematics
Mohammad Shahrouzi
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
(2018)
Article
Mathematics
Mohammad Shahrouzi
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
(2020)
Article
Mathematics, Applied
Mohammad Shahrouzi
Summary: In this paper, a class of Lame inverse source problem with variable-exponent nonlinearities is studied. It is shown that solutions decay as time goes to infinity under certain conditions, and blow up in finite time in the absence of a damping term under other conditions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Hazal Yuksekkaya, Erhan Piskin, Jorge Ferreira, Mohammad Shahrouzi
Summary: This article discusses the existence and nonexistence of solutions for a viscoelastic wave equation with time delay and variable exponents on the damping and on source term. By combining the Banach contraction mapping principle and the Faedo-Galerkin method under suitable assumptions on the variable exponents m(.) and p(.), we obtain the existence of weak solutions. Under specific conditions, solutions with negative initial energy are shown to be nonexistence.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Applied
Mohammad Shahrouzi, Jorge Ferreira, Erhan Piskin
Summary: This paper studies the stability of solutions for a double-Kirchhoff type viscoelastic inverse source problem with nonlocal degenerate damping term and variable-exponent nonlinearities. By introducing suitable auxiliary functionals and a Lyapunov functional, it is proven that the solutions of the problem are asymptotically stable in the appropriate range of variable exponents.
RICERCHE DI MATEMATICA
(2022)
Article
Mathematics
Mohammad Shahrouzi
Summary: In this paper, we study a variable-exponent fourth-order viscoelastic equation and prove that under suitable conditions, the solutions will grow exponentially with positive initial energy level. Our result improves and extends earlier findings in the literature, such as those by Mahdi and Hakem.
FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS
(2022)
Article
Mathematics, Applied
Mohammad Shahrouzi, Jorge Ferreira, Erhan Piskin, Khaled Zennir
Summary: In this work, the behavior of solutions for a non-linear viscoelastic fourth-order p(x)-Laplacian equation with non-linear boundary conditions is studied. Under suitable data conditions, the global existence of solutions, general decay, and blow-up results with positive and negative initial energy have been proven.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Mohammad Shahrouzi, Jorge Ferreira, Faramarz Tahamtani
Summary: This study investigates the global existence, asymptotic stability, and blow up of solutions for a nonlinear viscoelastic fourth-order (p(x), q(x))-Laplacian equation with variable-exponent nonlinearities. The study first proves the global existence of solutions, and then shows that the solutions are asymptotically stable with suitable initial data. Moreover, under certain conditions, it is proven that there exists a finite time period in which some solutions exhibit both positive and negative initial energies.
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN
(2023)
Article
Mathematics
Mohammad Shahrouzi
Summary: This study investigates the global existence and asymptotic stability of solutions for a class of nonlinear viscoelastic higher-order p(x)-Laplacian equation. The results extend and improve upon earlier findings in the literature.
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA
(2023)
Article
Mathematics
Mohammad Shahrouzi
Summary: In this paper, we investigate the blow-up phenomena of solutions to the nonlinear r(x)-Laplacian Lame equation in a smoothly bounded domain, with variable exponents and initial data conditions.
INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Mohammad Shahrouzi, Firoozeh Kargarfard
Summary: This paper investigates a Kirchhoff type equation with variable exponent nonlinearities, demonstrating that solutions blow up in a finite time under appropriate conditions and arbitrary positive initial energy. Furthermore, the upper bound estimate of the blowup time is obtained.
JOURNAL OF APPLIED ANALYSIS
(2021)
Article
Mathematics, Applied
Mohammad Shahrouzi
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS
(2020)
Article
Mathematics, Applied
Mohammad Shahrouzi
ANNALI DI MATEMATICA PURA ED APPLICATA
(2017)
Article
Mathematics, Applied
Junfeng Cao, Ke Chen, Huan Han
Summary: This paper proposes a two-stage image segmentation model based on structure tensor and fractional-order regularization. In the first stage, fractional-order regularization is used to approximate the Hausdorff measure of the MS model. The solution is found using the ADI scheme. In the second stage, thresholding is used for target segmentation. The proposed model demonstrates superior performance compared to state-of-the-art methods.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Dylan J. Oliver, Ian W. Turner, Elliot J. Carr
Summary: This paper discusses a projection-based framework for numerical computation of advection-diffusion-reaction (ADR) equations in heterogeneous media with multiple layers or complex geometric structures. By obtaining approximate solutions on a coarse grid and reconstructing solutions on a fine grid, the computational cost is significantly reduced while accurately approximating complex solutions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Nathan V. Roberts, Sean T. Miller, Stephen D. Bond, Eric C. Cyr
Summary: In this study, the time-marching discontinuous Petrov-Galerkin (DPG) method is applied to the Vlasov equation for the first time, using backward Euler for a Vlasov-Poisson discretization. Adaptive mesh refinement is demonstrated on two problems: the two-stream instability problem and a cold diode problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Yizhi Sun, Zhilin Sun
Summary: This work investigates the convexity of a specific class of positive definite probability measures and demonstrates the preservation of convexity under multiplication and intertwining product. The study reveals that any integrable function on an interval with a polynomial expansion of fast absolute convergence can be decomposed into a pair of positive convex interval probabilities, simplifying the study of interval distributions and discontinuous probabilistic Galerkin schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Bhagwan Singh, Komal Jangid, Santwana Mukhopadhyay
Summary: This paper examines the prediction of bending characteristics of nanoscale materials using the Moore-Gibson-Thompson thermoelasticity theory in conjunction with the nonlocal strain gradient theory. The study finds that the stiffness of the materials can be affected by nonlocal and length-scale parameters, and the aspect ratios of the beam structure play a significant role in bending simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Guoliang Wang, Bo Zheng, Yueqiang Shang
Summary: This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method, and the post-processing technique. The algorithm generates a global continuous approximate solution using the partition of unity method and improves the smoothness of the solution by adding an extra coarse grid correction step. It has good parallel performance and is validated through theoretical error estimates and numerical test examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Hao Xu, Zeng-Qi Wang
Summary: Fluid flow control problems are crucial in industrial applications, and solving the optimal control of Navier-Stokes equations is challenging. By using Oseen's approximation and matrix splitting preconditioners, we can efficiently solve the linear systems and improve convergence.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhengya Yang, Xuejuan Chen, Yanping Chen, Jing Wang
Summary: This paper focuses on the high-order stable numerical solutions of the time-space fractional diffusion equation. The Fourier spectral method is used for spatial discretization and the Spectral Deferred Correction (SDC) method is used for numerical solutions in time. As a result, a high-precision numerical discretization scheme for solving the fractional diffusion equation is obtained, and the convergence and stability of the scheme are proved. Several numerical examples are presented to demonstrate the effectiveness and feasibility of the proposed numerical scheme.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
