Single shock solution for non convex scalar conservation laws
Adimurthi, Shyam Sundar Ghoshal
TL;DR
This paper investigates the conditions under which a single shock forms in finite time for solutions to one-dimensional scalar conservation laws with general flux functions, using structural and characteristic analysis.
Contribution
It provides a necessary and sufficient condition linking initial data to flux for shock formation, based on flux structure and characteristic curves analysis.
Findings
Characterizes initial data leading to shock formation
Establishes a precise condition for shock emergence
Analyzes flux structure and characteristics in detail
Abstract
In this paper we study the finite time emergence of one shock for the solution of scalar conservation laws in one space dimension with general flux f . We give a necessary and sufficient condition to the initial data connecting to flux. The proof relies on the structure theorem for the linear degenerate flux and the finer analysis of characteristic curves.
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Taxonomy
TopicsNavier-Stokes equation solutions · Cosmology and Gravitation Theories · Geometric Analysis and Curvature Flows