A Note on the Jump Conditions for Systems of Conservation Laws

• Published in: Studies in applied mathematics (Cambridge) Vol. 110; no. 4; pp. 391 - 396
• Main Authors: Srinivasan, G. K., Sharma, V. D.
• Format: Journal Article
• Language: English
• Published: 350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK Blackwell Publishing, Inc 01.05.2003; Blackwell
• Subjects: Conservation laws; Electrostatics; Exact sciences and technology; Mathematical analysis; Mathematics; Partial differential equations; Sciences and techniques of general use; Singularities; Theorems; Water waves; Conservation law; Schwarztian distribution; Nonlinearity; Heaviside function; Lebesgue integral; Jumping; Non linear system; Rankine Hugoniot equation; Vector field; Jump condition; Equation system
• ISSN: 0022-2526; 1467-9590
• DOI: 10.1111/1467-9590.00244

In [1], the authors have demonstrated the effect on the Rankine–Hugoniot conditions for a system of conservation laws driven by a singular forcing function and have applied their results to a problem in water waves. We analyze here a similar problem in several space dimensions, in which the singularity in the forcing term involves a simple layer potential supported along the singularity locus. A classical theorem in electrostatics appears as a special case.