On the Cauchy problem of a 2 times 2 system of nonstrictly hyperbolic conservation laws

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:5515358

Kan, P T

Global existence for a 2 {times} 2 system of nonstrictly hyperbolic conservation law is established for data of arbitrary bounded variation. This result is obtained by proving a convergence theorem for the method of artificial viscosity applied to this system of conservation law. For this purpose, the method of compensated compactness and an analysis of the entropy functions are used. This system under consideration is a special case of a canonical class of 2 {times} 2 systems of conservation laws with quadratic flux functions possessing an isolated umbilic point (point of coinciding wave speeds where strict hyperbolicity fails) at the origin of the state space. These systems arise as model equations to equations used in oil reservoir simulations. Their wave curves and Riemann problem solutions are known to exhibit complexities not seen in any strictly hyperbolic systems. In this thesis, besides establishing global existence for a special system in the canonical class, general properties of a subclass are also investigated. The geometry of rarefaction wave curves are analytically studied and Riemann invariants are constructed. An L{sup {infinity}} bound (independent of the viscosity) for the solutions of the corresponding viscous systems are obtained. Also studied is the monotonicity properties of the wave speeds in the Riemann invariant plane.

• Research Organization: New York Univ., NY (United States)
• OSTI ID: 5515358
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
020300* -- Petroleum-- Drilling & Production
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ANALYTICAL SOLUTION
CAUCHY PROBLEM
CONSERVATION LAWS
CONVERGENCE
DATA
DATA ANALYSIS
ENGINEERING
ENTROPY
GEOMETRY
INFORMATION
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATHEMATICS
PHYSICAL PROPERTIES
RESERVOIR ENGINEERING
RIEMANN SPACE
SPACE
THERMODYNAMIC PROPERTIES
VISCOSITY