I would like to get a good reference to study Hugoniot Locus in conservation laws, maybe videos or PDF's.
Many thanks.
2026-03-26 11:04:30.1774523070
References on the Hugoniot locus of hyperbolic systems
72 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in REFERENCE-REQUEST
- Best book to study Lie group theory
- Alternative definition for characteristic foliation of a surface
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Random variables in integrals, how to analyze?
- Abstract Algebra Preparation
- Definition of matrix valued smooth function
- CLT for Martingales
- Almost locality of cubic spline interpolation
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- property of Lebesgue measure involving small intervals
Related Questions in PARTIAL-DIFFERENTIAL-EQUATIONS
- PDE Separation of Variables Generality
- Partial Derivative vs Total Derivative: Function depending Implicitly and Explicitly on Variable
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Harmonic Functions are Analytic Evan’s Proof
- If $A$ generates the $C_0$-semigroup $\{T_t;t\ge0\}$, then $Au=f \Rightarrow u=-\int_0^\infty T_t f dt$?
- Regular surfaces with boundary and $C^1$ domains
- How might we express a second order PDE as a system of first order PDE's?
- Inhomogeneous biharmonic equation on $\mathbb{R}^d$
- PDE: Determine the region above the $x$-axis for which there is a classical solution.
- Division in differential equations when the dividing function is equal to $0$
Related Questions in HYPERBOLIC-EQUATIONS
- what does mean a zero eigenvalue in a PDE?
- Solution of Burgers' equation
- Canonical form of PDE
- Introduction to characteristic surfaces and bicharacteristics
- Simple calculus
- Uniqueness and domain of dependence for wave equations.
- Goursat Problem Solution
- Method of Characteristics for traffic flow equation
- Lax-Wendroff method for linear advection - Stability analysis
- Help deriving Lax-Wendroff scheme for advection equation $u_t+c(x)u_x = 0$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
This topic is well introduced in the books by R.J. LeVeque (1,2). Currently, the same author is working on the book project Riemann Problems and Jupyter Solutions (see the homepage), where §1.7 on shallow water equations presents Hugoniot loci in an interactive manner. The presentation of the Riemann solution of the $p$-system --- which is one of the standard example of such a graphical resolution, along with the shallow water equations --- in the book by E. Godlewski and P.-A. Raviart (3) is also quite instructive and easy to follow. Maybe more instructive but less easy to get in touch with would be the book by J. Smoller (4), or even the book by C.M. Dafermos (5).
(1) R.J. LeVeque, Numerical Methods for Conservation Laws, Birkhäuser, 1992. doi:10.1007/978-3-0348-8629-1
(2) R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge university press, 2002. doi:10.1017/CBO9780511791253
(3) E. Godlewski, P.-A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer, 1996. doi:10.1007/978-1-4612-0713-9
(4) J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer, 1994. doi:10.1007/978-1-4612-0873-0
(5) C.M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, 4th ed., Springer, 2016. doi:10.1007/978-3-662-49451-6