By Constantine M. Dafermos
ISBN-10: 354064914X
ISBN-13: 9783540649144
This masterly exposition of the mathematical concept of hyperbolic method legislation brings out the intimate reference to continuum thermodynamics, emphasizing concerns during which the research could display whatever in regards to the physics and, in go back, the underlying actual constitution might direct and force the research. The reader must have a undeniable mathematical sophistication and be accustomed to (at least) the rudiments of the qualitative conception of partial differential equations, while the necessary notions from continuum physics are brought from scratch. the objective crew of readers may include (a) specialists within the mathematical idea of hyperbolic platforms of conservation legislation who desire to find out about the relationship with classical physics; (b) experts in continuum mechanics; (c) specialists in numerical research who with to benefit the underlying mathematical conception; and (d) analysts and graduate scholars who search creation to the speculation of hyperbolic platforms of conservation legislation.
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Extra info for Hyperbolic Conservation Laws in Continuum Physics (Grundlehren der mathematischen Wissenschaften)
Sample text
Applying the assumption, inherent in the physical approach, that macrophenomenologically the mechanical behavior of all materials is qualitatively the same, and that the differences between materials stemming from their variety are quantitative and are reflected in the magnitude of the parameters of their constitutive equations. 3. Assuming that not only is each phase in itself considered homogeneous or quasi-homogeneous, but that the various phases are quasi-homogeneously distributed throughout the mixture.
But the problems are there and provide an inspiring challenge to the research mind. Bjerum (1969), in the president's opening address of the Seventh International Conference of SOMEFE, admits: ... we must nevertheless, admit that there is also available a relatively large number of carefully studied cases in which the classical approach of soil mechanics proved to be a failure. In these cases a comparison between a carefully performed prediction and the actual behavior has shown discrepancies so large that they could not be explained by inhomogeneities of the soil strata, nor by the scattering of the test results.
At a lower level of investigation the measuring techniques become more refined, therefore more involved, difficult and sometimes technically impossible. 3. At a higher level of investigation the mathematical formulation becomes simpler. 4. At a higher level of investigation there are less assumptions concerning boundary conditions, and they are obtained from the lower levels. 5. In principle, all three levels of investigation should lead to the same quantitative results. 6. In reality, the higher the level the more of the overall behavior of the material it comprehends, therefore the resulting theory is a better quantitative approximation; however, the physical interactions in it become obscured.
Hyperbolic Conservation Laws in Continuum Physics (Grundlehren der mathematischen Wissenschaften) by Constantine M. Dafermos
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