Work

Global non-selfsimilar Riemann solutions for multi-dimensional scalar conservation laws with time-dependent nonlinear source terms

Year: 2026

Type: article

Abstract: In this paper, we are concerned with the global non-selfsimilar Riemann solutions for the multi-dimensional scalar conservation law with a time-dependent nonlinear source term 𝑔 ⁡ ( 𝑡 , 𝑢 ) , where the Riemann-type initial data consist of two constant states separated by a curved initial discontinuity, namely an ( 𝑛 − 1 ) -dimensional smooth manifold. For this Riemann problem, under the Lipschitz relating condition on the source term 𝑔 ⁡ ( 𝑡 , 𝑢 ) in (8) and Condition ℋ in (9) , we construct global the non-selfsimilar Riemann solutions, including non-selfsimilar shock waves and non-selfsimilar rarefaction waves, in which the shock surface and the solution in the rarefaction region are expressed by implicit functions, respectively. Furthermore, we prove the uniqueness by showing that these global non-selfsimilar Riemann solutions are Kruzkov entropy solutions. Finally, we present two examples to illustrate the global structures of multi-dimensional non-selfsimilar shock waves and rarefaction waves.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2026.114795

Authors: Yuan-An Zhao, Gao-Wei Cao, Xiao-Zhou Yang

Institutions: Hubei University for Nationalities, Hetao Institute of Mathematics and Interdisciplinary Sciences, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, CAS

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: National Natural Science Foundation of China, Natural Science Foundation of Hubei Province, Key Science and Technology Research Project in Jiangxi Province Department of Education