Relevant bibliographies by topics / Uniqueness and qualitative properties of entire solutions

Academic literature on the topic 'Uniqueness and qualitative properties of entire solutions'

Author: Grafiati
Published: 10 March 2023
Last updated: 11 March 2023

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Journal articles on the topic "Uniqueness and qualitative properties of entire solutions"

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Poláčik, Peter. "On uniqueness of positive entire solutions and other properties of linear parabolic equations." Discrete & Continuous Dynamical Systems - A 12, no. 1 (2005): 13–26. http://dx.doi.org/10.3934/dcds.2005.12.13.

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Ieşan, Dorin, and Ramon Quintanilla. "Qualitative properties in strain gradient thermoelasticity with microtemperatures." Mathematics and Mechanics of Solids 23, no. 2 (January 5, 2017): 240–58. http://dx.doi.org/10.1177/1081286516680860.

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This paper is devoted to the strain gradient theory of thermoelastic materials whose microelements possess microtemperatures. The work is motivated by an increasing use of materials which possess thermal variation at a microstructure level. In the first part of this paper we deduce the system of basic equations of the linear theory and formulate the boundary-initial-value problem. We establish existence, uniqueness, and continuous dependence results by the means of semigroup theory. Then, we study the one-dimensional problem and establish the analyticity of solutions. Exponential stability and impossibility of localization are consequences of this result. In the case of the anti-plane problem we derive uniqueness and instability results without assuming the positivity of the mechanical energy. Finally, we study equilibrium theory and investigate the effects of a concentrated heat source in an unbounded body.
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Nguyen, Phuoc-Tai, and Hoang-Hung Vo. "Existence, uniqueness and qualitative properties of positive solutions of quasilinear elliptic equations." Journal of Functional Analysis 269, no. 10 (November 2015): 3120–46. http://dx.doi.org/10.1016/j.jfa.2015.09.003.

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Suárez, Antonio. "Nonnegative solutions for a heterogeneous degenerate competition model." ANZIAM Journal 46, no. 2 (October 2004): 273–97. http://dx.doi.org/10.1017/s1446181100013845.

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AbstractThis paper deals with the existence, uniqueness and qualitative properties of nonnegative and nontrivial solutions of a spatially heterogeneous Lotka-Volterra competition model with nonlinear diffusion. We give conditions in terms of the coefficients involved in the setting of the problem which assure the existence of nonnegative solutions as well as the uniqueness of a positive solution. In order to obtain these results we employ monotonicity methods, singular spectral theory and a fixed point index.
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Hernández, Eduardo, and Jianhong Wu. "Existence, Uniqueness and Qualitative Properties of Global Solutions of Abstract Differential Equations with State-Dependent Delay." Proceedings of the Edinburgh Mathematical Society 62, no. 3 (January 30, 2019): 771–88. http://dx.doi.org/10.1017/s001309151800069x.

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AbstractWe study the existence, uniqueness and qualitative properties of global solutions of abstract differential equations with state-dependent delay. Results on the existence of almost periodic-type solutions (including, periodic, almost periodic, asymptotically almost periodic and almost automorphic solutions) are proved. Some examples of partial differential equations with state-dependent delay arising in population dynamics are presented.
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Cabré, Xavier, and Yannick Sire. "Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions." Transactions of the American Mathematical Society 367, no. 2 (October 1, 2014): 911–41. http://dx.doi.org/10.1090/s0002-9947-2014-05906-0.

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Bhakta, Mousomi, and Debangana Mukherjee. "Nonlocal scalar field equations: Qualitative properties, asymptotic profiles and local uniqueness of solutions." Journal of Differential Equations 266, no. 11 (May 2019): 6985–7037. http://dx.doi.org/10.1016/j.jde.2018.11.023.

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Berestycki, Henri, and Alessandro Zilio. "Predators–prey models with competition, Part I: Existence, bifurcation and qualitative properties." Communications in Contemporary Mathematics 20, no. 07 (October 14, 2018): 1850010. http://dx.doi.org/10.1142/s0219199718500104.

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We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their asymptotic properties in time, showing that the solutions have different behavior depending on the choice of the parameters. We also construct heterogeneous stationary solutions and study the limits of strong competition and abundant resources. We then use these information to study some properties such as the existence of solutions that maximize the total population of predators. We prove that in some regimes the optimal solution for the size of the total population contains two or more groups of competing predators.
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Shakhmurov, Veli, and Rishad Shahmurov. "The regularity properties and blow-up of the solutions for improved Boussinesq equations." Electronic Journal of Qualitative Theory of Differential Equations, no. 89 (2021): 1–21. http://dx.doi.org/10.14232/ejqtde.2021.1.89.

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In this paper, we study the Cauchy problem for linear and nonlinear Boussinesq type equations that include the general differential operators. First, by virtue of the Fourier multipliers, embedding theorems in Sobolev and Besov spaces, the existence, uniqueness, and regularity properties of the solution of the Cauchy problem for the corresponding linear equation are established. Here, L p -estimates for a~solution with respect to space variables are obtained uniformly in time depending on the given data functions. Then, the estimates for the solution of linearized equation and perturbation of operators can be used to obtain the existence, uniqueness, regularity properties, and blow-up of solution at the finite time of the Cauchy for nonlinear for same classes of Boussinesq equations. Here, the existence, uniqueness, L p -regularity, and blow-up properties of the solution of the Cauchy problem for Boussinesq equations with differential operators coefficients are handled associated with the growth nature of symbols of these differential operators and their interrelationships. We can obtain the existence, uniqueness, and qualitative properties of different classes of improved Boussinesq equations by choosing the given differential operators, which occur in a wide variety of physical systems.
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Guo, Zongming, Xia Huang, Dong Ye, and Feng Zhou. "Qualitative properties of Hénon type equations with exponential nonlinearity." Nonlinearity 35, no. 1 (December 3, 2021): 492–512. http://dx.doi.org/10.1088/1361-6544/ac3925.

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Abstract We are interested in the qualitative properties of solutions of the Hénon type equations with exponential nonlinearity. First, we classify the stable at infinity solutions of Δu + |x| α e u = 0 in R N , which gives a complete answer to the problem considered in Wang and Ye (2012 J. Funct. Anal. 262 1705–1727). Secondly, existence and precise asymptotic behaviours of entire radial solutions to Δ2 u = |x| α e u are obtained. Then we classify the stable and stable at infinity radial solutions to Δ2 u = |x| α e u in any dimension.
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Dissertations / Theses on the topic "Uniqueness and qualitative properties of entire solutions"

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BORDONI, SARA. "Nonlinear elliptic problems in the Heisenberg group." Doctoral thesis, 2018. http://hdl.handle.net/2158/1121183.

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The aim of this Ph.D. thesis is to present new results concerning the study of nonlinear elliptic problems in the context of the Heisenberg group. We deal with different problems, but the common thread consists in extending to a more general setting, the Heisenberg group, results proved in the Euclidean case. This generalization process in the Heisenberg framework implies a series of technical difficulties, that force the use of new key theorems.
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Alwan, Mohamad. "Qualitative Properties of Stochastic Hybrid Systems and Applications." Thesis, 2011. http://hdl.handle.net/10012/6243.

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Hybrid systems with or without stochastic noise and with or without time delay are addressed and the qualitative properties of these systems are investigated. The main contribution of this thesis is distributed in three parts. In Part I, nonlinear stochastic impulsive systems with time delay (SISD) with variable impulses are formulated and some of the fundamental properties of the systems, such as existence of local and global solution, uniqueness, and forward continuation of the solution are established. After that, stability and input-to-state stability (ISS) properties of SISD with fixed impulses are developed, where Razumikhin methodology is used. These results are then carried over to discussed the same qualitative properties of large scale SISD. Applications to automated control systems and control systems with faulty actuators are used to justify the proposed approaches. Part II is devoted to address ISS of stochastic ordinary and delay switched systems. To achieve a variety stability-like results, multiple Lyapunov technique as a tool is applied. Moreover, to organize the switching among the system modes, a newly developed initial-state-dependent dwell-time switching law and Markovian switching are separately employed. Part III deals with systems of differential equations with piecewise constant arguments with and without random noise. These systems are viewed as a special type of hybrid systems. Existence and uniqueness results are first obtained. Then, comparison principles are established which are later applied to develop some stability results of the systems.
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Book chapters on the topic "Uniqueness and qualitative properties of entire solutions"

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Malinowski, Marek T. "Modeling with Stochastic Fuzzy Differential Equations." In Advances in Computational Intelligence and Robotics, 150–72. IGI Global, 2014. http://dx.doi.org/10.4018/978-1-4666-4991-0.ch008.

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In the chapter, the author considers an approach used in the studies of stochastic fuzzy differential equations. These equations are new mathematical tools for modeling uncertain dynamical systems. Some qualitative properties of their solutions such as existence and uniqueness are recalled, and stability properties are shown. Here, the solutions are continuous adapted fuzzy stochastic processes. The author considers some examples of applications of stochastic fuzzy differential equations in modeling real-world phenomena.
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Conference papers on the topic "Uniqueness and qualitative properties of entire solutions"

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Hohl, Andreas, Carsten Hohl, and Christian Herbig. "A Combined Analytical and Numerical Approach to Analyze Mud Motor Excited Vibrations in Drilling Systems." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-42144.

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Severe vibrations in drillstrings and bottomhole assemblies can be caused by cutting forces at the bit or mass imbalances in downhole tools. One of the largest imbalances is related to the working principle of the so-called mud motor, which is an assembly of a rotor that is maintained by the stator. One of the design-related problems is how to minimize vibrations excited by the mud motor. Simulation tools using specialized finite element methods (FEM) are established to model the mechanical behavior of the structure. Although finite element models are useful for estimating rotor dynamic behavior and dynamic stresses of entire drilling systems they do not give direct insight how parameters affect amplitudes and stresses. Analytical models show the direct influence of parameters and give qualitative solutions of design related decisions. However these models do not provide quantitative numbers for complicated geometries. An analytical beam model of the mud motor is derived to calculate the vibrational amplitudes and capture basic dynamic effects. The model shows the direct influence of parameters of the mud motor related to the geometry, material properties and fluid properties. The analytical model is compared to the corresponding finite element model. Vibrational amplitudes are discussed for different modes and parameter changes. Finite element models of the entire drilling system are used to verify the findings from the analytical model using practical applications. The results are compared to time domain and statistical data from laboratory and field measurements.
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