16 citations · 55 across the 15 of their papers we have counts for
15 papers
The Riemann Problem for a 3x3 Generalized Chaplygin Gas System with Variable Pressure
Thomas Allen, Ella Kim, Jonathan Nunes +2
We consider the Riemann problem for a 3x3 system of conservation laws with generalized Chaplygin pressure , , where the pressure depends on an…
Dynamic Response of a Finite Circular Plate on an Elastic Half-Space Using the Truncated Lamb Kernel
Greyson Meares, Sage Meiling, Charis Tsikkou
We develop an exact operator formulation for the dynamic interaction between a finite circular elastic plate and an elastic half-space. Classical analyses, beginning with Lamb's re…
Non-isentropic cavity flow for the multi-d compressible Euler system
Helge Kristian Jenssen, Charis Tsikkou
We rigorously construct non-isentropic and self-similar multi-d Euler flows in which a central cavity (vacuum region) collapses. While isentropic flows of this type have been analy…
An Analysis of the Riemann Problem for a System of Keyfitz-Kranzer Type Balance Laws With a Time-Dependent Source Term
Josh Culver, Aubrey Ayres, Evan Halloran +3
We consider a system consisting of one conservation law and one balance law with a time-dependent source term, and provide a comprehensive analysis of Riemann solutions, including…
An Analysis of the Riemann Problem for a System of Keyfitz-Kranzer Type Conservation Laws Using Shadow Waves and Dafermos Regularization
Josh Culver, Aubrey Ayres, Evan Halloran +3
We consider a system of two conservation laws and provide a detailed description of both classical and non-classical self-similar Riemann solutions. In particular, we demonstrate t…
Solving the Wave Equation on Discrete Time Scales
Davis Funk, Charis Tsikkou
This paper presents a solution to an initial value problem for the 1-dimensional wave equation on time scales through the application of a Fourier transform and its inverse via con…
An Analysis of a 2x2 Keyfitz-Kranzer Type Balance System with Varying Generalized Chaplygin Gas
Jack Frew, Nigel Keyser, Ethan Kim +4
We consider a system of two balance laws of Keyfitz-Kranzer type with varying generalized Chaplygin gas, which exhibits negative pressure and is a product of a function of time and…
Radially Symmetric Non-isentropic Euler flows: continuous blowup with positive pressure
Helge Kristian Jenssen, Charis Tsikkou
Guderley's 1942 work on radial shock waves provides cases of self-similar Euler flows exhibiting blowup of primary (undifferentiated) flow variables: a converging shock wave invade…
Multi-d Isothermal Euler Flow: Existence of unbounded radial similarity solutions
Helge Kristian Jenssen, Charis Tsikkou
We show that the multi-dimensional compressible Euler system for isothermal flow of an ideal, polytropic gas admits global-in-time, radially symmetric solutions with unbounded ampl…
On similarity flows for the compressible Euler system
Helge Kristian Jenssen, Charis Tsikkou
Radial similarity flow offers a rare instance where concrete inviscid, multi-dimensional, compressible flows can be studied in detail. In particular, there are flows of this type t…
Two Dimensional Riemann Problems for the Nonlinear Wave System: Rarefaction Wave Interactions
Eun Heui Kim, Charis Tsikkou
We analyze rarefaction wave interactions of self-similar transonic irrotational flow in gas dynamics for the two dimensional Riemann problems. We establish the existence result of…
On convergence of exterior solutions to radial Cauchy solutions for
Helge Kristian Jenssen, Charis Tsikkou
Consider the Cauchy problem for the 3-d linear wave equation with radial initial data , . A standard result gives that…
Radial solutions to the Cauchy problem for as limits of exterior solutions
Helge Kristian Jenssen, Charis Tsikkou
We consider the strategy of realizing the solution of a Cauchy problem with radial data as a limit of radial solutions to initial-boundary value problems posed on the exterior of v…
Singular Shocks in a Chromatography Model
Charis Tsikkou
We consider a system of two equations that can be used to describe nonlinear chromatography and produce a coherent explanation and description of the unbounded solutions (singular…
Analysis of 2+1 diffusive-dispersive PDE arising in river braiding
Saleh Tanveer, Charis Tsikkou
We present local existence and uniqueness results for the following dispersive diffusive equation due to P. Hall arising in modeling of river braiding: $$u_{yyt} - γu_{xxx} -…