The multiplication of distributions in the study of delta shock waves for zero-pressure gasdynamics system with energy conservation laws

Sen, Anupam; Sekhar, T. Raja

doi:10.1007/s11587-021-00565-5

Cited by 5 publications

(2 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From (22) we have, D[ṽ(t)] = g(t)τ γ(t) δ, (27) and from (20), it follows g(0)τ γ(0) δ = mδ, which means that γ(0) = 0 and g(0) = m. Then, from (26) we get a(0) + b(0)H = u 1 + (u 2 − u 1 )H and a(0) = u 1 and b(0) = u 2 − u 1 follows. From ( 21) and ( 22) we get respectively…”

Section: Article Pubsaiporg/aip/jmpmentioning

confidence: 99%

“…Certainly this is one of the reasons for which several authors begun to adopt this method (see Refs. [18][19][20][21][22][23][24][25][26][27][28][29][30]. Another reason regards to important simplifications: the Rankine-Hugoniot shock conditions and their multiple generalizations are not necessary and, as much as we know, the final result is the same (see Refs.…”

Section: Introduction and Contentsmentioning

confidence: 99%

See 1 more Smart Citation

Products of distributions and the problem of galactic rotation

Sarrico

2024

Journal of Mathematical Physics

View full text Add to dashboard Cite

In the present paper we study the nonlinear system ut + [ϕ(u)]x + v = 0, vt + ψ(u)vx = 0 as a model for the one-dimensional dynamics of dark matter. We prove that under certain conditions this system, such as the Gurevich-Zybin system, can also explain why the observed rotation speed (relative to the galactic center) of stars near galactic halos do not coincide with what it is expected in classical mechanics. The solutions are obtained in fully explicit formulas, in a convenient space of distributions, without using any result within the classical framework. For such purpose we use the α-solution concept which is defined within a product of distributions. Such a concept generalizes the classical solution concept and for evolution equations may also be seen as an extension of the weak solution concept to the nonlinear setting.

show abstract

Section: Article Pubsaiporg/aip/jmpmentioning

confidence: 99%

Section: Introduction and Contentsmentioning

confidence: 99%

Products of distributions and the problem of galactic rotation

Sarrico

2024

Journal of Mathematical Physics

View full text Add to dashboard Cite

show abstract

Delta Shocks as Solutions of Conservation Laws with Discontinuous Moving Source

Sarrico

2024

J Dyn Diff Equat

View full text Add to dashboard Cite

Multiplication of distributions and singular waves in several physical models

Domingos

2024

European Journal of Mathematics

View full text Add to dashboard Cite

We study of a Riemann problem for a one-dimensional $$2\hspace{1.111pt}{\times }\hspace{1.111pt}2$$ 2 × 2 system of conservation laws, which includes some particular cases of known physical systems, such as the pressureless gas dynamics system, Euler equations for isentropic flow, the Brio system, and the shallow water system. The main results of this study reveal the emergence of shock waves and delta shock waves as explicit solutions. We use the concept of $$\alpha $$ α -solution defined in the setting of a product of distributions not defined by approximation. Notably, this study does not assume any classical results about conservation laws, presenting a simpler and more general framework for constructing singular solutions to other equations or systems. Additionally, this paper includes several comments on the four physical systems mentioned, along with formulas for multiplying distributions and evaluating the compositions of a function with a distribution.

show abstract

The multiplication of distributions in the study of delta shock waves for zero-pressure gasdynamics system with energy conservation laws

Cited by 5 publications

References 34 publications

Products of distributions and the problem of galactic rotation

Products of distributions and the problem of galactic rotation

Delta Shocks as Solutions of Conservation Laws with Discontinuous Moving Source

Multiplication of distributions and singular waves in several physical models

Contact Info

Product

Resources

About