,, 222-237. for nonlinear wave equations Nonlinear waves - R.Agemi the of. 3) which has to satisfy the following integral equation.
Partial Differential Equations (1983). Instructions for use Title Global existence of nonlinear elastic waves Author(s) Agemi, R. Takamura, Blow-up boundaries and rates for nonlinear wave equations A.
Remarks on the asymptotic behavior of the cubic nonlinear Klein-Gordon equations in one space dimension Sunagawa, Hideaki, Differential and Integral Equations, ; Global existence for the cubic nonlinear Schrödinger equation in lower order Sobolev spaces Hayashi, Nakao and Naumkin, Pavel I. For this reason, we modify the approximation by adding a higher-order term. Nonlinear Waves, Gakuto International Series, Mathematical Sciences and Applications, 542pp. Hopf equation (inviscid Burgers equation): &92;(u_t+uu_x=0&92;). Proof of the Main Theorem First, we shall follow some basic facts of a representation formula of a solution of (1.
First, the initial deformation must be a small dis-placement from equilibrium, in this case a prestressed homogeneous dilation of the reference configuration, and equally important, the nonlinear terms must. -, Long-time existence of solutions of nonlinear wave equations, Ph. , Journal of Geometry and Symmetry in. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc.
Mitidieri 3 except for the critical case. On certain integral related equations to nonlinear wave equations Rentaro AGEMI, K&92;^oji KUBOTA and Hiroyuki TAKAMURA (Recei. Nonlinear PDE and Stochastics (1998), 43-86. Takamura, Remarks on representations of solutions to the wave equa-tions, Mathematical Research Note 94-004, Institute of Mathematics, University of Tsukuba (June, 1994). Based on this variational structure, we suggest a null condition which is a kind of structural condition on the nonlinearity in order to stop the formation of finite time singularities of local smooth Nonlinear waves - R.Agemi solutions. , Communications in Mathematical Sciences, Recursion Operators and Reductions of Integrable Equations on Symmetric Spaces Gerdjikov, Vladimir S.
Kubo, Global small amplitude solutions of nonlinear hyperbolic systems with a critical exponent under the null condition. Introduction This article considers th. , 619-645. Velo, On the existence of the wave operators for a class of nonlinear. They used the operator Sin order to extract a decaying factor from the elastic wave operator.
Ginibre, An Introduction to Nonlinear Schrödinger Equations in Nonlinear waves, R. Kubotafor their valuable comment. KLAINERMAN, The null condition and global existence to nonlinear wave equations Lectures in Applied Mathematics, 23, 293-326, 1986. The closed form solutions are given by way of example only, as nonlinear wave equations often have many possible solutions. A stability result for solitary waves in nonlinear dispersive equations Akers, Benjamin and Milewski, Paul A. Chen --The null condition and global existence of solutions to systems of wave equations with different speeds / R.
AxPgSac1997 J. Hokkaido Mathematical Journal Vol. thesis, Courant Institute of Mathematical Sciences, New York University, 1986. Agemi, Blow-up of solutions to nonlinear wave equations in two space dimensions,, Manuscripta Math. Contents: Mathematical aspects of supersonic flow past wings / S. Palmieri, Nonexistence of global solutions for the semilinear Moore - Gibson - Thompson equation in the conservative case, Discrete Contin. Annals of Mathematics,, 849874 Nonresonance and global existence of prestressed nonlinear elastic waves By Thomas C.
Agemi on his 70th birthday) Yin Yin Su Win and Yoshio Tsutsumi (Received Janu; Revised J) Abstract. Let u_&92;epsilon be a C^2-solution to (1. We study the unconditional uniqueness of solution for the Cauchy problem of the nonlinear Schr¨odinger equation. Christodoulou, Global solutions of nonlinear hyperbolic equations for small initial. A non-exhaustive selection of well known 1D nonlinear wave equations and their closed-form solutions is given below.
,, 153. In this paper, we first give the explicit variational structure of the nonlinear elastic waves for isotropic, homogeneous, hyperelastic materials in 2-D. Agemi and Professor K. John, “ Formation of singularities in one-dimensional nonlinear wave propagation,” Commun. Weighted L∞ and L1 estimates for solutions to the classical wave equation in three space dimensions title=Weighted L∞ and L1 estimates for solutions to the classical wave equation in three space Nonlinear waves - R.Agemi dimensions, author=S. Citation Hokkaido University Preprint Series in Mathematics, 463, 1-57 Issue Date. Nonlinear wave equation solutions. Yokoyama, The null condition and Nonlinear waves - R.Agemi global existence of solutions to systems of wave equations with different speeds, Adv.
SIDERIS, The null condition and global existence of nonlinear elastic waves, Inven. (in press) (). of the nonlinear Schr¨odinger equation (Dedicated to Prof. TakamuraOn certain integral equations related to nonlinear wave equations. , and Valchev, Tihomir I.
This estimate is enough for the global existence for nonlinear problem. Georgiev & E. Takamura, Blow-up for semilinear damped wave equations with sub-Strauss exponent in the scattering case, Nonlinear Anal.
Ozawa, GAKUTO International Series, Mathematical Sciences and Applications, 267—272, (1996). Ozawa, Long range scattering for nonlinear Schr¨odinger and Hartree equations in space in dimension n ‚ 2, Commun. Sachs, On the transverse instability of solitary waves in the Kadomtsev-Petviashvili equation, Phys. Agemi, Blow-up of solutions to nonlinear wave equations in two space dimensions, Manuscripta Math. ISBN:: OCLC Number:: Description: 1 online resource (vii 351 pages) : illustrations.
Takamura 2 for a simplified proof. This kind of time growth of the highest Sobolev norms of the generalized energy also appears in the work of Sideris 17,18 and Agemi 1 for the 3D compressible nonlinear elastic waves, of. Unfortunately, we can not apply their method to our case due to the lack of such a rpus ID:. - an arbitrary direction of propagation in a cube face and both geometrically and physically nonlinear model, - three selected derections of. Agemi, “ Global existence of nonlinear elastic waves. Yokoyama The null conditions and global existence of solutions to systems of wave equations with different propagation speeds.
3D nonlinear wave equations in three space dimensions, global existence hinges on two basic assumptions. Klainerman, journal=Communications on Pure and Applied Mathematics, year=1984. In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. Lin, On the Incompressible Limit of the Slightly Compressible Viscous Fluid Flows, In NONLINEAR WAVES, Proceedings of the 4th Mathematical Society of Japan International Research Institute Vol II, Hokkaito University, (eds. A detailed description is given on the large time behavior of scattering solutions to the Cauchy problem for nonlinear Schrödinger equations with repulsive interactions in the short-range case with. Agemi; Weighted uniform decay estimates for solutions to isotropic elastic wave equations / pp. However, their method requires that the nonlinearity has a divergence structure. R.Agemi It contains ten articles, each of which discusses a very recent result obtained by the author.
The existence of the critical curve for p-q systems of nonlinear wave equations was already established by D. A unique global smooth solution, Critical exponent, DataGlobalSmﬃ Existence, Small Data Blow-up, Null condition, Diﬀerent propagation speeds 1 Quasilinear Case In this section we study the quasilinear case. , 48, World Scientific, Singapore ( 1998), pp. These estimates can be used to prove a series of weighted Strichartz and KSS type estimates, for wave equations on asymptotically flat space-time. ), Advances in Nonlinear Partial Differential Equations and Stochastics, Series on Adv. Tiba; An analytic approach to a generalized Naghdi shell model / pp. Agemi, Global existence of nonlinear elastic waves, preprint, Hokkaido Univ, 1998.
the nonlinear elastic waves with the critical exponent. This Special Issue aims to show the latest advances in nonlinear waves and differential equations, whether the results are theoretical or numerical. Google Scholar 2 R.
More Nonlinear Waves - R. Then, we are able to obtain a lower bound of the lifespan which is expressed in terms of initial data and a coefficient in the nonlinearity. However, it does not satisfy the nonlinear elastic wave equation in a suitable sense. , Mikhailov, Alexander V. Instructions for use Title Global existence of nonlinear elastic waves Author(s) Agemi, R. Lyaghfouri; A free boundary problem for a flow of fresh and salt groundwater with nonlinear Darcy&39;s law. ear wave equations, Hokkaido. Glassey, MathReview to "Global behavior of solutions to nonlinear wave equations in three space dimensions" of Sideris,, Comm.
The existence of the critical curve for p-q systems of nonlinear wave equations was already established by D. Giga, "Nonlinear Partial Differential Equations, Asymptotic behaviour of solutions and self-similar solutions" (Hisenkei Henbibun Houteishiki - Kai no Zenkinkyodo to Jiko Soji Kai. Namely, we assume (1. Google Scholar 3. Yokoyama --Scaling limits for large systems of interacting particles / K. Takamura forthe lifespan in two space dimensions. Presentation of explicit nonlinear plane waves&39; elasktodynamics equations for a cubic crystal in the case - an arbitrary direction of propagation and a geometrically nonlinear but physically linear model. We show the uniqueness of solution in C(0, T.
Takamura, Nonexistence of global solutions of nonlinear wave equa-tions with weak time-dependent damping related to Glassey’s conjecture. Then we apply the space-time estimates to obtain the lower bound of the lifespan when the nonlinear exponents &92;begindocument$ p $&92;enddocument and &92;begindocument$ q&92;ge 2 $&92;enddocument. ,, 241-276.
Del Santo & V. Any results in this talk are based on a joint paper with R. , Differential and Integral Equations,. The theory and application of nonlinear waves has attracted great interest and needs to be further studied. 13 Kôji Kubota, Existence of a global solution to a semi-linear wave equation with initial data of noncompact support in low space dimensions, Hokkaido Math.
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