18 problems

ZND-limit stability conjecture for system detonations
arXiv@arxiv
Let a system detonation have an associated ZND detonation and a component Neumann shock. Gas-dynamical stability refers to stability of this component Neumann shock, while hyperbol…
Conjectureopendetonation-waves hyperbolic-systems stability
0
Agafonov–Ferapontov algebraicity conjecture for focal varieties
arXiv@arxiv
Agafonov–Ferapontov conjecture. Such a congruence always has an algebraic focal variety, possibly reducible and singular.
Conjectureopenalgebraic-geometry hyperbolic-systems line-congruences
1
Main Conjecture, Part 1 on persistence of solutions to Hamiltonian perturbations
arXiv@arxiv
Let $v=v(x,t)$ be a smooth solution of the unperturbed equation … defined for all $x\in\boldsymbol{R}$ and $0\leq t<t_0$ , and monotone in $x$ for every $t$ . Let $H_f$ be the Hamilt…
Conjectureopenhamiltonian-pdes hyperbolic-systems singular-perturbation
0
Conjecture on the algorithmic completeness of generalized Laplace transformations
arXiv@arxiv
Algorithmic completeness conjecture. The new procedure should provide an algorithm for generalized factorization and a closed-form complete solution, precisely in the sense of Tsar…
Conjectureopenfactorization hyperbolic-systems partial-differential-equations
0
Global hyperbolicity of spline shallow water moment systems
arXiv@arxiv
Let a spline shallow water moment system be regularized around a linear profile by the transformation described above, yielding a hyperbolic system matrix for systems based on an…
Conjectureopenhyperbolic-systems shallow-water-equations spline-methods
1
Ruggeri's asymptotic convergence conjecture for hyperbolic relaxation systems
arXiv@arxiv
Consider the hyperbolic system of $N$ partial differential equations … … where $\mathbf{F}^0(\mathbf{V},\mathbf{W})$ and $\mathbf{F}^i(\mathbf{V},\mathbf{W})$ are column vectors in…
Conjectureopenhyperbolic-systems relaxation-systems riemann-problems
0
Positive boundary dissipation conjecture for BIBO stability of hBCS
arXiv@arxiv
Positive boundary dissipation conjecture. If $\widetilde{W}_B R_0^{-1} \Sigma \left(\widetilde{W}_B R_0^{-1}\right)^* > 0$ , then the hBCS is BIBO stable. In the setting where the d…
Conjectureopenbibo-stability boundary-control-systems hyperbolic-systems
0
Intermediate-domain well-posedness conjecture for genuinely nonlinear $2\times 2$ hyperbolic systems
arXiv@arxiv
Intermediate-domain well-posedness conjecture. The Cauchy problem for a genuinely nonlinear $2\times 2$ hyperbolic system with ${\bf L}^\infty$ initial data is well posed within an…
Conjectureopenhyperbolic-conservation-laws hyperbolic-systems well-posedness
0
Ruggeri's hyperbolicity conjecture for true physical systems
arXiv@arxiv
Ruggeri's conjecture. True physical systems are of hyperbolic type.
Conjectureopenhyperbolic-systems rational-extended-thermodynamics viscoelasticity
0
Exact controllability criterion for linear one-dimensional hyperbolic systems in L^q
arXiv@arxiv
Exact controllability criterion. The conditions in Theorem 1.2, namely
Conjectureopencontrollability control-theory hyperbolic-systems
0
Generalization of the methodology to hyperbolic-hyperbolic thermoelastic systems
arXiv@arxiv
The classical thermoelastic system is a hyperbolic-parabolic coupled system whose large-time asymptotic profiles can be studied using methods for third-order-in-time evolution equa…
Conjectureopenasymptotic-analysis hyperbolic-systems thermoelasticity
1
The bilateral-actuation conjecture for predictive boundary control
arXiv@arxiv
Bilateral-actuation conjecture. Bilateral control with actuators available at both boundaries might lead to smaller prediction errors and, consequently, better robustness margins b…
Conjectureopenboundary-control hyperbolic-systems robust-control
0
The artificial-viscosity explanation for additional numerical decay
arXiv@arxiv
Consider a finite-volume approximation of a linear hyperbolic system on a spatial and temporal grid, with piecewise-constant reconstruction $\mathbf{U}(t,x)$ and theoretical expone…
Conjectureopenartificial-viscosity hyperbolic-systems numerical-analysis
0
Hyperbolic-system ansatz for the functions f and r
arXiv@arxiv
Consider the first-order hyperbolic system for functions $f$ and $r$ on the relevant $(x,y)$ -domain, and suppose the initial conditions at $y=0$ determine $h_1,h_2,h_3$ . Hyperbolic…
Conjectureopenhyperbolic-systems partial-differential-equations
0
Uniqueness of the thermodynamic entropy solution for the hyperbolic system
arXiv@arxiv
Let $\bar u=(\bar r,\bar p)$ be a limit solution of the hyperbolic system with boundary conditions, satisfying the Clausius inequality … for all $t\in[0,T]$ , where $W(t)$ is the wo…
Conjectureopenentropy-solutions hyperbolic-systems thermodynamics
0
Conjecture on non-strictly hyperbolic non-locally bi-Hamiltonian systems
arXiv@arxiv
A non-singular (semisimple) non-locally bi-Hamiltonian system of hydrodynamic type has a diagonal matrix of velocities … Such systems are strictly hyperbolic when their eigenvalues…
Conjectureopenbi-hamiltonian-systems hydrodynamic-type-systems hyperbolic-systems
0
BV structure conjecture for velocity without convexity assumptions
arXiv@arxiv
BV-structure conjecture. The bounded-variation structure of the velocity remains valid in the general case without a convexity assumption, or, more specifically, when the eigenvalu…
Conjectureopenbounded-variation gas-chromatography hyperbolic-systems
0
Validity of strong stability for general piecewise genuinely nonlinear isotherms
arXiv@arxiv
Strong-stability conjecture. The result proved in the paper—namely, the stratified representation of the velocity, propagation of large-amplitude high-frequency oscillations in the…
Conjectureopengas-chromatography hyperbolic-systems weak-convergence
0