The δ′ wave solution to a totally degenerate system of conservation laws

Y Pang, L Shao, Y Wen, J Ge - Chaos, Solitons & Fractals, 2022 - Elsevier
We focus on the Riemann solutions to a totally degenerate system of conservation laws with
repeated eigenvalues and repeated eigenvectors. Based on the theory of multiplication of …

The Riemann problem for the one-dimensional isentropic Euler system under the body force with varying gamma law

C Shen, M Sun - Physica D: Nonlinear Phenomena, 2023 - Elsevier
The exact Riemann solutions are presented in fully explicit forms for the one-dimensional
isentropic Euler system of gas dynamics with the body force, in which the shock and …

Interactions of delta shock waves in a pressureless hydrodynamic model

Y Wang, M Sun - Applicable Analysis, 2023 - Taylor & Francis
The Riemann problem for a pressureless hydrodynamic model is solved explicitly, whose
solution is either a contact-vacuum-contact wave or a delta shock wave to connect the left …

[HTML][HTML] The Riemann problem for pressureless compressible fluid system with time-and space-dependent external force

Y Pang, Y Wen, C Xu - Results in Physics, 2023 - Elsevier
We concern with Riemann problem for an one-dimensional pressureless compressible fluid
system with time-and space-dependent external force. Under the concept of α-solution to …

The multiplication of distributions in the study of delta shock wave for a hyperbolic system of Temple class

C Shen, M Sun - International Journal of Mathematics, 2021 - World Scientific
The Riemann problem for a hyperbolic system of conservation laws belonging to Temple
class is considered within frame of α-solutions based on the concept of solutions defined in …

Multiplication of distributions and singular waves in several physical models

AR Domingos - European Journal of Mathematics, 2024 - Springer
We study of a Riemann problem for a one-dimensional 2× 2 system of conservation laws,
which includes some particular cases of known physical systems, such as the pressureless …

Riemann solutions and wave interactions for a hyperbolic system derived from the steady 2D Helmholtz equation under a paraxial assumption

C Shen - Applied Mathematics Letters, 2025 - Elsevier
Two kinds of exact Riemann solutions for a hyperbolic system arising from the steady 2D
Helmholtz equation under a paraxial assumption are constructively achieved by using either …

On Existence and Admissibility of Singular Solutions for Systems of Conservation Laws

H Kalisch, D Mitrovic - International Journal of Applied and Computational …, 2022 - Springer
A weak notion of solution for systems of conservation laws in one dimension is put forward.
In the framework introduced here, it can be shown that the Cauchy problem for any n× n …

The propagation and collision behavior of δ′ waves in a model of three partial differential equations

Y Pang, C Xu - Zeitschrift für angewandte Mathematik und Physik, 2024 - Springer
Both propagation and collision behavior of δ′ waves in a model of three partial differential
equations are investigated. These are Cauchy problems for this model with initial values …

[HTML][HTML] On the viscosity approximation of conservation laws with non-crossing discontinuous flux

KH Karlsen, D Mitrović, M Nedeljkov - Journal of Differential Equations, 2025 - Elsevier
We investigate a conservation law characterized by a discontinuous flux, given by u t+∂ x (f
L (u) H (− x)+ f R (u) H (x))= 0, where max u∈ K⁡ f L (u)< max u∈ K⁡ f R (u), for any …