关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

A criterion is given for the convergence of numerical solutions of the Navier-Stokes equations in two dimensions under steady conditions. The criterion applies to all cases, of steady viscous flow in two dimensions and shows that if the local ' mesh Reynolds number ', based on the size of the mesh used in the solution, exceeds a certain fixed value, the numerical solution will not converge.

On the Navier-Stokes equations

5. M. Green, J. Schwarz, and E. Witten, Superstring theory, Cambridge Univ. Press, 1987. 6. J. Isenberg, P. Yasskin, and P. Green, Non-self-dual gauge fields, Phys. Lett. 78B (1978), 462-464. 7. B. Kostant, Graded manifolds, graded Lie theory, and prequantization, Differential Geometric Methods in Mathematicas Physics, Lecture Notes in Math., vol. 570, SpringerVerlag, Berlin and New York, 1977. 8. C. LeBrun, Thickenings and gauge fields, Class. Quantum Grav. 3 (1986), 1039-1059. 9. , Thickenings and conformai gravity, preprint, 1989. 10. C. LeBrun and M. Rothstein, Moduli of super Riemann surfaces, Commun. Math. Phys. 117(1988), 159-176. 11. Y. Manin, Critical dimensions of string theories and the dualizing sheaf on the moduli space of (super) curves, Funct. Anal. Appl. 20 (1987), 244-245. 12. R. Penrose and W. Rindler, Spinors and space-time, V.2, spinor and twistor methods in space-time geometry, Cambridge Univ. Press, 1986. 13. R. Ward, On self-dual gauge fields, Phys. Lett. 61A (1977), 81-82. 14. E. Witten, An interpretation of classical Yang-Mills theory, Phys. Lett. 77NB (1978), 394-398. 15. , Twistor-like transform in ten dimensions, Nucl. Phys. B266 (1986), 245-264. 16. , Physics and geometry, Proc. Internat. Congr. Math., Berkeley, 1986, pp. 267302, Amer. Math. Soc, Providence, R.I., 1987.

Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Roger Temam)

Diffusion and ecological problems : mathematical models

In 1982, the Belgian Pilots' Guild raised the question of what effect exposure to radar radiation--for example, that encountered in passing a pilot launch's radar--might have on the human body. Recapitulating investigations of this question, this article states that in 25 years of experience with radar, there have been no known incidents of pilots being affected by radar waves. In the future, however, involvement by some pilots with Vessel Traffic Service shore-based radar could affect pilots somewhat differently from limited exposure to pilot launch radar. Pilots who find themselves in new working conditions close to an emitting source should exercise care all times.

About heat waves

Introduction.- 1. Global solutions to wave equations - existence theorems.- 2. L^p - L^q-decay estimates for the linear we equation.- 3. Linear symmetric hyperbolic systems.- 3.1 Energy estimates.- 3.2 A global existence theorem.- 3.3 Remarks on other methods.- 4. Some inequalities.- 5. Local existence for quasilinear symmetric hyperbolic.- 6. High energy estimates.- 7. Weighted a priori estimates.- 8. Global solutions to wave equations - proofs.- 8.1 Proof of Theorem 1.1.- 8.2 Proof ot Theorem 1.2.- 9. Other methods.- 10. Development of singularities.- 11. More evolutions equations.- 11.1 Equations of elasiticity.- 11.1.1 Initially isotropic media in R^3.- 11.1.2 Initially cubic media in R^3.- 11.2 Heat equations.- 11.3 Equations of thermoelasticity.- 11.4 Schrodinger equations.- 11.5 Klein-Gordon equations.- 11.6 Maxwell equations.- 11.7 Plate equations.- 12. Further aspects and questions.- 13. Evolution equations in waveguides.- 13.1 Nonlinear wave equations.- 13.1.1 Linear part.- 13.1.2 Nonlinear part.- 13.2. Schrodinger equations.- 13.3. Equations of elasticity and Maxwell equations.- 13.4 General waveguides.- Appendix.- A. Interpolation.- B. The Theorem of Cauchy-Kowalevsky.- C. A local existence theorem for hyperbolic-parabolic systems References Notation Index.

Lectures on nonlinear evolution equations

Energy decay for Timoshenko systems of memory type

http://www.im.ufrj.br/~rivera/Art_Pub/RackeR01.pdf

Mildly dissipative nonlinear Timoshenko systems—global existence and exponential stability☆

We consider hyperbolic Timoshenko-type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction. While exponential stability under the Fourier law of heat conduction holds, it turns out that the coupling via the Cattaneo law does not yield an exponentially stable system. This seems to be the first example that a removal of the paradox of infinite propagation speed inherent in Fourier’s law by changing to the Cattaneo law causes a loss of the exponential stability property. Actually, for systems with history, the Fourier law keeps the exponential stability known for the pure Timoshenko system without heat conduction, but introducing the Cattaneo coupling even destroys this property.

/pdf/on-the-stability-of-damped-timoshenko-systems-cattaneo-4dd3c3jltp.pdf

On the stability of damped Timoshenko systems - Cattaneo versus Fourier law

https://www.math.uni-konstanz.de/~racke/dvidat/m32.pdf

Reinhard Racke

Papers

Lectures on nonlinear evolution equations

Energy decay for Timoshenko systems of memory type

Mildly dissipative nonlinear Timoshenko systems—global existence and exponential stability☆

On the stability of damped Timoshenko systems - Cattaneo versus Fourier law

A note on stability in three-phase-lag heat conduction