Dissertation Information for Raoofi MohammadrezaNAME:
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SCHOOL: ADVISORS: COMMITTEE MEMBERS: MPACT Status: Incomplete - Not_Inspected Title: Asymptotic behavior of perturbed viscous shock profiles Abstract: We investigate the L p asymptotic behavior (1 ≤ p ≤ ∞) of a perturbation of a Lax or overcompressive type shock wave solution to a system of conservation law in one dimension. The system of the equations can be strictly parabolic, or partially parabolic (real viscosity case, e.g., compressible Navier-Stokes equations or equations of Magnetohydrodynamics). We use known pointwise Green function bounds for the linearized equation around the shock to show that the perturbation of such a solution can be decomposed into a part corresponding to shift in shock position or shape, a part which is the sum of diffusion waves, i.e., the solutions to a viscous Burger's equation, conserving the initial mass and connecting away from the shock profile in outgoing modes, and another part which is more rapidly decaying in any L p norm. |
MPACT Scores for Raoofi MohammadrezaA = 0 Advisors and Advisees Graph |