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
Meiirkhan B. Borikhanov, Berikbol T. Torebek
Summary: In this paper, we study an inhomogeneous pseudo-parabolic equation with nonlocal nonlinearity and prove the blow-up result for the critical case using the test function method. We also improve upon the integral result obtained by Bandle et al. (2000) and answer an open question posed by Zhou (2020).
APPLIED MATHEMATICS LETTERS
(2022)
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
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
Tae Gab Ha, Sun-Hye Park
Summary: This paper discusses a nonlinear wave equation with boundary damping and source terms of variable exponent nonlinearities. The aim of this work is to prove the nonexistence of global solutions for the equation with both nonnegative and negative initial energy.
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
(2022)
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
Kh Zennir, H. Dridi, S. Alodhaibi, S. Alkhalaf
Summary: The most important behavior in evolution systems is the blow-up phenomena due to its wide applications in modern science. This article discusses the finite time blowup that arises under appropriate conditions, and investigates the nonsolvability of boundary value problems for damped pseudoparabolic differential equations with variable exponents. The novelty lies in the case of variable nonlinearities p and q, which adds scientific interest to the problem.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Mathematics, Applied
Jorge A. Esquivel-Avila
Summary: This article discusses the nonexistence of global solutions of a class of nonlinear second-order evolution equations with a memory term, and introduces a new positive invariance set to improve the results in the literature.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2021)
Article
Mathematics
Natalia Kolkovska, Milena Dimova, Nikolai Kutev
Summary: In this article, the Cauchy problem for Klein-Gordon equations with combined power-type nonlinearities is investigated. The coefficients in the nonlinearities depend on the space variable and are sign preserving functions except for one coefficient that may change sign. The structure of the Nehari manifold is studied completely. Necessary and sufficient conditions for the nonexistence of a global solution for subcritical initial energy are given using the sign of the Nehari functional. New sufficient conditions for finite time blow up of weak solutions are proposed when the energy is positive, with one condition being independent of the sign of the scalar product of the initial data. Uniqueness of the weak solutions is also proven under slightly more restrictive assumptions for the powers of the nonlinearities.
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
Sun-Sig Byun, Wontae Kim
Summary: The established global Calderon-Zygmund theory for the weak solution of the p-Laplacian system ensures the desired estimates hold for every q greater than or equal to p, providing insight into the properties of the solutions for further analysis and research.
MATHEMATISCHE ANNALEN
(2022)
Article
Mathematics, Applied
Adel M. Al-Mahdi, Mohammad M. Al-Gharabli, Maher Nour, Mostafa Zahri
Summary: This paper considers a viscoelastic wave equation with boundary damping and a variable exponent source term. The existence of global solutions is proved, and optimal and general decay estimates are established depending on the relaxation function and the nature of the variable exponent nonlinearity. Two numerical tests are conducted to demonstrate the theoretical results. This study generalizes and enhances existing literature results and is of significant importance compared to previous literature results with constant or variable exponents in the domain.
Article
Mathematics
Adel. M. M. Al-Mahdi, Mohammad. M. M. Al-Gharabli, Mostafa Zahri
Summary: Strong vibrations can cause damage to structures and materials. The Tacoma Narrows Bridge collapsed due to sudden oscillation changes caused by resonance, and other bridges have collapsed for the same reason. Dampers and modifications are used to stabilize bridges and prevent resonance during earthquakes and winds. This study focuses on a nonlinear viscoelastic plate equation with variable exponents, and establishes decay results based on the relaxation function and nonlinearity. Numerical tests are conducted to illustrate the theoretical results, extending and generalizing previous works.
MATHEMATISCHE NACHRICHTEN
(2023)
Article
Mathematics
Qi Li, Yuzhu Han, Tianlong Wang
Summary: This paper investigates a critical biharmonic elliptic problem under certain assumptions, and using the Mountain Pass Lemma, it proves the existence of at least one nontrivial weak solution and also obtains a nonexistence result.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
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
Mohammad Shahrouzi
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2016)
Article
Mathematics, Applied
Mohammad Shahrouzi
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2018)
Article
Mathematics
Mohammad Shahrouzi
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
(2018)
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)
