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131.
Gilberto Flores 《Journal of Differential Equations》2009,247(5):1529-1590
This paper studies the stability of a family of traveling wave solutions to the system proposed by Lane et al. [D.C. Lane, J.D. Murray, V.S. Manoranjan, Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilization waves on eggs, IMA J. Math. Appl. Med. Biol. 4 (4) (1987) 309-331], to model a pair of mechanochemical phenomena known as post-fertilization waves on eggs. The waves consist of an elastic deformation pulse on the egg's surface, and a free calcium concentration front. The family is indexed by a coupling parameter measuring contraction stress effects on the calcium concentration. This work establishes the spectral, linear and nonlinear orbital stability of these post-fertilization waves for small values of the coupling parameter. The usual methods for the spectral and evolution equations cannot be applied because of the presence of mixed partial derivatives in the elastic equation. Nonetheless, exponential decay of the directly constructed semigroup on the complement of the zero eigenspace is established. We show that small perturbations of the waves yield solutions to the nonlinear equations decaying exponentially to a phase-modulated traveling wave. 相似文献
132.
Bin He 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):6011-6018
In this paper, an independent variable transformation is introduced to solve the modified Camassa-Holm equation using the bifurcation theory and the method of phase portrait analysis. Some peakons, solitary waves and periodic waves are found and their exact parametric representations in explicit form and in implicit form are obtained. 相似文献
133.
Shih-sen Chang H.W. Joseph Lee Chi Kin Chan 《Nonlinear Analysis: Theory, Methods & Applications》2009
In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed point for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. As applications, at the end of the paper we utilize our results to study the optimization problem and some convergence problem for strictly pseudocontractive mappings. The results presented in the paper extend and improve some recent results of Yao and Yao [Y.Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput. 186 (2) (2007) 1551–1558], Plubtieng and Punpaeng [S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point problems of nonlinear mappings and monotone mappings, Appl. Math. Comput. (2007) doi:10.1016/j.amc.2007.07.075], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for Equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2006) 506–515], Su, Shang and Qin [Y.F. Su, M.J. Shang, X.L. Qin, An iterative method of solution for equilibrium and optimization problems, Nonlinear Anal. (2007) doi:10.1016/j.na.2007.08.045] and Chang, Cho and Kim [S.S. Chang, Y.J. Cho, J.K. Kim, Approximation methods of solutions for equilibrium problem in Hilbert spaces, Dynam. Systems Appl. (in print)]. 相似文献
134.
In this paper we deal with the mixed initial-boundary value problem of Dirichlet type for the nonlinear elastodynamic system outside a domain. The local existence of solutions to this problem is proved by iteration. 相似文献
135.
In this paper we are working with a generalized Kolosov-Muskhelishvili formula. This representation formula expresses the elastic displacements of a solid body in terms of two monogenic functions. Known
polynomial systems of monogenic functions are used to construct a basis of polynomial solutions to the Lamé system from linear
elasticity.
Received: October, 2007. Accepted: February, 2008. 相似文献
136.
C. S. Jog 《Journal of Elasticity》2006,82(2):175-192
We present a solution for the tensor equation TX + XT
T
= H, where T is a diagonalizable (in particular, symmetric) tensor, which is valid for any arbitrary underlying vector space dimension n. This solution is then used to derive compact expressions for the derivatives of the stretch and rotation tensors, which in turn are used to derive expressions for the material time derivatives of these tensors. Some existing expressions for n = 2 and n = 3 are shown to follow from the presented solution as special cases. An alternative methodology for finding the derivatives of diagonalizable tensor-valued functions that is based on differentiating the spectral decomposition is also discussed. Lastly, we also present a method for finding the derivatives of the exponential of an arbitrary tensor for arbitrary n. 相似文献
137.
R. J. Weinacht 《Journal of Elasticity》2006,83(2):105-111
For a bounded region in a Helmholtz/Weyl decomposition of the Sobolev space is given,with orthogonality with respect to the strain-energy inner product of elasticity (anisotropic or isotropic). 相似文献
138.
We investigate the linear system of thermoelasticity, consisting of an elasticity equation and a heat conduction equation, in a waveguide Ω=(0,1)×Rn−1, with certain boundary conditions. We consider the cases of homogeneous and inhomogeneous systems and prove decay estimates of the solutions, which are a key ingredient to showing the global existence of solutions to non-linear thermoelasticity, after having decomposed the solutions into various parts. We also give a simplified proof to the representation of the solutions to the Cauchy problem of thermoelasticity. 相似文献
139.
For a contraction A on a Hilbert space H, we define the index j(A) (resp., k(A)) as the smallest nonnegative integer j (resp., k) such that ker(I−Aj∗Aj) (resp., ker(I−Ak*Ak)∩ker(I−AkAk∗)) equals the subspace of H on which the unitary part of A acts. We show that if , then j(A)?n (resp., k(A)?⌈n/2⌉), and the equality holds if and only if A is of class Sn (resp., one of the three conditions is true: (1) A is of class Sn, (2) n is even and A is completely nonunitary with ‖An−2‖=1 and ‖An−1‖<1, and (3) n is even and A=U⊕A′, where U is unitary on a one-dimensional space and A′ is of class Sn−1). 相似文献
140.
This obituary for Israel Gohberg consists of a general introduction, separate contributions of the six authors, all of whom worked closely with him, and a final note. The material gives an impression of the life of this great mathematician, of his monumental impact in the areas he worked in, of how he cooperated with colleagues, and of his ability to stimulate people in their mathematical activities. 相似文献