共查询到20条相似文献,搜索用时 15 毫秒
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Nikolai A. Kudryashov Dmitry I. Sinelshchikov 《Applied mathematics and computation》2010,217(1):414-421
Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions of nonlinear evolution equation of the fourth order are found by means of the simplest equation method. Properties of nonlinear waves in a liquid with gas bubbles are discussed. 相似文献
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Georgia Karali Tonia Ricciardi 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):4271-4281
We construct special sequences of solutions to a fourth order nonlinear parabolic equation of Cahn-Hilliard/Allen-Cahn type, converging to the second order Allen-Cahn equation. We consider the evolution equation without boundary, as well as the stationary case on domains with Dirichlet boundary conditions. The proofs exploit the equivalence of the fourth order equation with a system of two second order elliptic equations with “good signs”. 相似文献
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This paper deals with a GALERKIN-based multi-scale time integration of a viscoelastic rope model. Using HAMILTON's dynamical formulation, NEWTON's equation of motion as a second-order partial differential equation is transformed into two coupled first order partial differential equations in time. The considered finite viscoelastic deformations are described by means of a deformation-like internal variable determined by a first order ordinary differential equation in time. The corresponding multi-scale time-integration is based on a PETROV-GALERKIN approximation of all time evolution equations, leading to a new family of time stepping schemes with different accuracy orders in the state variables. The resulting nonlinear algebraic time evolution equations are solved by a multi-level NEWTON-RAPHSON method. Realizing this transient numerical simulation, we also demonstrates a parallelized solution of the viscous evolution equation in CUDA©. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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The fourth order average vector field (AVF) method is applied to solve
the "Good" Boussinesq equation. The semi-discrete system of the "good" Boussinesq
equation obtained by the pseudo-spectral method in spatial variable, which is a
classical finite dimensional Hamiltonian system, is discretized by the fourth order
average vector field method. Thus, a new high order energy conservation scheme of
the "good" Boussinesq equation is obtained. Numerical experiments confirm that the
new high order scheme can preserve the discrete energy of the "good" Boussinesq
equation exactly and simulate evolution of different solitary waves well. 相似文献
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Hernán R. Henríquez 《Semigroup Forum》2013,87(2):277-297
In this paper the existence of solutions of a nonautonomous abstract Cauchy problem of second order is considered. Assuming appropriate conditions on the operator of the equation, we establish the existence of mild solutions and, in some cases, we construct an evolution operator associated to the homogeneous equation. Using this evolution operator we obtain existence of solutions for the inhomogeneous equation. Finally, we apply our results to study the existence of solutions of the nonautonomous wave equation. 相似文献
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We develop a space-time fractional Schrödinger equation containing Caputo fractional derivative and the quantum Riesz fractional operator from a space fractional Schrödinger equation in this paper. By use of the new equation we study the time evolution behaviors of the space-time fractional quantum system in the time-independent potential fields and two cases that the order of the time fractional derivative is between zero and one and between one and two are discussed respectively. The space-time fractional Schrödinger equation with time-independent potentials is divided into a space equation and a time one. A general solution, which is composed of oscillatory terms and decay ones, is obtained. We investigate the time limits of the total probability and the energy levels of particles when time goes to infinity and find that the limit values not only depend on the order of the time derivative, but also on the sign (positive or negative) of the eigenvalues of the space equation. We also find that the limit value of the total probability can be greater or less than one, which means the space-time fractional Schrödinger equation describes the quantum system where the probability is not conservative and particles may be extracted from or absorbed by the potentials. Additionally, the non-Markovian time evolution laws of the space-time fractional quantum system are discussed. The formula of the time evolution of the mechanical quantities is derived and we prove that there is no conservative quantities in the space-time fractional quantum system. We also get a Mittag-Leffler type of time evolution operator of wave functions and then establish a Heisenberg equation containing fractional operators. 相似文献
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对具有非线性源项和非线性扩散项的热传导方程建立格子Boltzmann求解模型.在演化方程中增加了两个关于源项分布函数的微分算子,对演化方程实施Chapman-Enskog展开.通过对演化方程的进一步改进,恢复出具有高阶截断误差的宏观方程.对不同参数选取下的非线性热传导方程进行了数值模拟,数值解与精确解吻合得很好.该模型也可以用于同类型的其他偏微分方程的数值计算中. 相似文献
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We study the martensitic transformation with a phase field model, where we consider the Bain transformation path in a small strain setting. For the order parameter, interpolating between an austenitic parent phase and martensitic phases, we use a Ginzburg-Landau evolution equation, assuming a constant mobility. In [1], a temperature dependent separation potential is introduced. We use this potential to extend the model in [2], by considering a transient temperature field, where the temperature is introduced as an additional degree of freedom. This leads to a coupling of both the evolution equation of the order parameter and the mechanical field equations (in terms of thermal expansion) with the heat equation. The model is implemented in FEAP as a 4-node element with bi-linear shape functions. Numerical examples are given to illustrate the influence of the temperature on the evolution of the martensitic phase. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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We study a class of dynamic thermal sub-differential contact problems with friction, for long memory visco-elastic materials, without the clamped condition, which can be put into a general model of system defined by a second order evolution inequality, coupled with a first order evolution equation. We present and establish an existence and uniqueness result, by using general results on first order evolution inequality, with monotone operators and fixed point methods. Finally a fully discrete scheme for numerical approximations is provided, and corresponding various numerical computations in dimension two will be given. 相似文献
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Hernán R. Henríquez 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(10):3333-3352
In this paper the existence of solutions of a non-autonomous abstract retarded functional differential equation of second order with infinite delay is considered. Assuming the existence of an evolution operator corresponding to the associate abstract Cauchy problem of second order, we establish the existence of mild solutions of the functional equation. Furthermore, we study the existence of classical solutions of the abstract Cauchy problem of second order and we apply these results to establish the existence of classical solutions of the functional equation. Finally, we apply our results to study the existence of solutions of the non-autonomous wave equation with delay. 相似文献
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二阶线性发展方程初值问题的某些推广 总被引:1,自引:0,他引:1
本文用压缩半群理论讨论了二阶线性发展方程组的初值问题;还用解析半群讨论了一类变系数的二阶线性发展方程的初值问题,使这一类初值问题的可解性与含t的算子的一阶线性发展方程解的理论统一起来,这是数学力学中的一类重要方程。 相似文献
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In this paper we study a dynamical system which consists of the Cauchy problem for a nonlinear evolution equation of first order coupled with a nonlinear time-dependent variational–hemivariational inequality with constraint in Banach spaces. The evolution equation is considered in the framework of evolution triple of spaces, and the inequality which involves both the convex and nonconvex potentials. We prove existence of solution by the Kakutani–Ky Fan fixed point theorem combined with the Minty formulation and the theory of hemivariational inequalities. We illustrate our findings by examining a nonlinear quasistatic elastic frictional contact problem for which we provide a result on existence of weak solution. 相似文献
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Hernán R. Henríquez Verónica Poblete Juan C. Pozo 《Journal of Mathematical Analysis and Applications》2014
In this paper we establish the existence of mild solutions for a non-autonomous abstract semi-linear second order differential equation submitted to nonlocal initial conditions. Our approach relies on the existence of an evolution operator for the corresponding linear equation and the properties of the Hausdorff measure of non-compactness. 相似文献
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We consider a boundary value problem for a nonlinear differential equation which arises in an option pricing model with transaction costs. We apply the method of upper and lower solutions in order to obtain solutions for the stationary problem. Moreover, we give conditions for the existence of solutions of the general evolution equation. 相似文献
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Robert M. Yamaleev 《Journal of Mathematical Analysis and Applications》2006,322(2):815-824
Generator of the complex algebra within the framework of general formulation obeys the quadratic equation. In this paper we explore multicomplex algebra with the generator obeying n-order polynomial equation with real coefficients. This algebra induces generalized trigonometry ((n+1)-gonometry), underlies of the nth order oscillator model and nth order Hamilton equations. The solution of an evolution equation generated by (n×n) matrix is represented via the set of (n+1)-gonometric functions. The general form of the first constant of motion of the evolution equation is established. 相似文献
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By introducing the fractional derivatives in the sense of Caputo, we use the adomian decomposition method to construct the approximate solutions for the cubic nonlinear fractional Schordinger equation with time and space fractional derivatives. The exact solution of the cubic nonlinear Schrodinger equation is given as a special case of our approximate solution. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equation. 相似文献
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给出了一种改进的截断展开法,利用此方法借助于计算机符号计算求得了Burgers方程和浅水长波近似方程组的精确解,其中包括孤子解,并讨论其具体应用.改进后的方法与以前的方法相比能得到方程的更多形式的精确解.所给出的改进的截断展开法也可以用来研究其它非线性发展方程的孤子解,是求非线性发展方程精确解的一种有效的直接方法. 相似文献