27 October at 19:00 MSK
We study the Cauchy problem to scalar conservation law with power flux function and unbounded initial data. We will focus on unbounded initial data of exponential type. We construct a generalized entropy solution with countably many shock waves in the entire half-plane t > 0. This solution is sign-alternating and does not satisfy the maximum principle. It is known that the Cauchy problem in the class of locally bounded functions may have several solutions. We describe all entropy solutions of this problem, which can be represented in a special form. It is shown that after the first discontinuity line, these solutions eventually exhibit the same behavior, and their non-uniqueness actually amounts to the choice of the first shock wave.
PhD Gargyants Lidia ( Bauman Moscow State Technical University, Moscow, Russian Federation).
Title of the talk: On Locally Bounded Solutions To One-dimensional Conservation Laws.