다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Let us consider the Cauchy problem for the quasilinear hyperbolic integro-differential equation

/pdf/on-the-well-posedness-of-the-kirchhoff-string-9bl91x1046.pdf

On the Well-Posedness of the Kirchhoff String

https://ir.nuk.edu.tw/bitstream/310360000Q/10885/2/main-fibering.pdf

The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions

Considered as rest points of ODE on L p , stationary vis- cous shock waves present a critical case for which standard semigroup methods do not suce to determine stability. More precisely, there is no spectral gap between stationary modes and essential spectrum of the linearized operator about the wave, a fact that precludes the usual analysis by decomposition into invariant subspaces. For this reason, there have been until recently no results on shock stability from the semigroup perspective except in the scalar or totally compressive case ((Sat), (K.2), resp.), each of which can be reduced to the standard semi- group setting by Sattinger's method of weighted norms. We overcome this diculty in the general case by the introduction of new, pointwise semigroup techniques, generalizing earlier work of Howard (H.1), Kapit- ula (K.1-2), and Zeng (Ze,LZe). These techniques allow us to do \hard" analysis in PDE within the dynamical systems/semigroup framework: in particular, to obtain sharp, global pointwise bounds on the Green's function of the linearized operator around the wave, sucient for the analysis of linear and nonlinear stability. The method is general, and should nd applications also in other situations of sensitive stability. Central to our analysis is a notion of \eective" point spectrum that can be extended to regions of essential spectrum. This turns out to be intimately related to the Evans function, a well-known tool for the spectral analysis of traveling waves. Indeed, crucial to our whole analy- sis is the \Gap Lemma" of (GZ,KS), a technical result developed origi- nally in the context of Evans function theory. Using these new tools, we can treat general over- and undercompressive, and even strong shock waves for systems within the same framework used for standard weak (i.e. slowly varying) Lax waves. In all cases, we show that stability is determined by the simple and numerically computable condition that the number of zeroes of the Evans function in the right complex half- plane be equal to the dimension of the stationary manifold of nearby traveling wave solutions. Interpreting this criterion in the conserva-

/pdf/pointwise-semigroup-methods-and-stability-of-viscous-shock-18j9i33z3i.pdf

Pointwise Semigroup Methods and Stability of Viscous Shock Waves

We introduce an elementary energy method for the Boltzmann equation based on a decomposition of the equation into macroscopic and microscopic components. The decomposition is useful for the study of time-asymptotic stability of nonlinear waves. The wave location is determined by the macroscopic equation. The microscopic component has an equilibrating property. The coupling of macroscopic and microscopic components gives rise naturally to the dissipations similar to those obtained by the Chapman-Enskog expansion. Our main result is the establishment of the positivity of shock profiles for the Boltzmann equation. This is shown by the time-asymptotic approach and the maximal principle for the collision operator.

Boltzmann Equation: Micro-Macro Decompositions and Positivity of Shock Profiles

This paper is concerned with the asymptotic behavior toward the rarefaction waves of the solution of a one-dimensional model system associated with compressible viscous gas If the initial data are suitably close to a constant state and their asymptotic values atx=±∞ are chosen so that the Riemann problem for the corresponding hyperbolic system admits the weak rarefaction waves, then the solution is proved to tend toward the rarefaction waves ast→+∞ The proof is given by an elementaryL
 2 energy method

Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas

Travelling wave solutions with shock profile for a one-dimensional model system associated with compressible viscous gas are investigated in terms of asymptotic stability. The travelling wave solution is proved to be asymptotically stable, provided the initial disturbance is suitably small and of zero constant component. The proof is given by the elementalL
 2 energy method.

On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas

It has been asserted that the damped wave equation has the diffusive structure as t→∞. In this paper we consider the Cauchy problem in 3-dimensional space for the linear damped wave equation and the corresponding parabolic equation, and obtain the Lp−Lq estimates of the difference of each solution, which represent the assertion precisely. Explicit formulas of the solutions are analyzed for the proof. The second aim is to apply the Lp−Lq estimates to the semilinear damped wave equation with power nonlinearity. If the power is larger than the Fujita exponent, then the time global existence of small weak solution is proved and its optimal decay order is obtained.

Lp-Lq estimates of solutions to the damped wave equation in 3-dimensional space and their application

This paper is concerned with the asymptotic behavior toward the rarefaction wave of the solution of a one-dimensional barotropic model system for compressible viscous gas. We assume that the initial data tend to constant states atx=±∞, respectively, and the Riemann problem for the corresponding hyperbolic system admits a weak continuous rarefaction wave. If the adiabatic constant γ satisfies 1≦γ≦2, then the solution is proved to tend to the rarefaction wave ast→∞ under no smallness conditions of both the difference of asymptotic values atx=±∞ and the initial data. The proof is given by an elementaryL
2-energy method.

https://projecteuclid.org/download/pdf_1/euclid.cmp/1104249319

Kenji Nishihara

Papers

Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas

On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas

Lp-Lq estimates of solutions to the damped wave equation in 3-dimensional space and their application

Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas

The Lp–Lq estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media