MATERIAL LAYOUTS IN SPACE-TIME AND FOCUSING OF MASS FLOWS DUE TO COLLISION OF CHARACTERISTICS

Abstract eng:
A collision of characteristics may become necessary in the context of optimal design in dynamics, particularly, in connection with optimal mass transport produced by the controllable velocity chart in spacetime that serves as a factor focusing the moving masses into a special location (possibly, into a point). The collision of characteristics means the immediate development of discontinuities, such as mass concentration, in solutions of the dynamic equations. Such discontinuities appear in a habitual construction of non-linear hyperbolic equations due to their originally non-linear character. But when the equations are originally assumed linear (which is a part of our concept), then the problem remains linear only if the characteristics do not collide. If they do, one expects the appearance of non-linearity of some sort, generated by the physics of material collisions. ...

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