A direct proof of the equivalence between the entropy solutions of conservation laws and viscosity solutions of Hamilton-Jacobi equations in one-space variable.
Page 1 Next
Displaying 1 – 20 of 34
A new kind of the solution of degenerate parabolic equation with unbounded convection term
Huashui Zhan (2015)
Open Mathematics
A new kind of entropy solution of Cauchy problem of the strong degenerate parabolic equation [...] is introduced. If u0 ∈ L∞(RN), E = {Ei} ∈ (L2(QT))N and divE ∈ L2(QT), by a modified regularization method and choosing the suitable test functions, the BV estimates are got, the existence of the entropy solution is obtained. At last, by Kruzkov bi-variables method, the stability of the solutions is obtained.
Application of Rothe's method to perturbed linear hyperbolic equations and variational inequalities
Jozef Kačur (1984)
Czechoslovak Mathematical Journal
Characteristic initial value problem for hyperbolic systems of second order differential equations
H. Müller zum Hagen (1990)
Annales de l'I.H.P. Physique théorique
Contact problems with given time-dependent friction force in linear viscoelasticity
Jiří Jarušek (1990)
Commentationes Mathematicae Universitatis Carolinae
Convergence of mass redistribution method for the one-dimensional wave equation with a unilateral constraint at the boundary
Farshid Dabaghi, Adrien Petrov, Jérôme Pousin, Yves Renard (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
This paper focuses on a one-dimensional wave equation being subjected to a unilateral boundary condition. Under appropriate regularity assumptions on the initial data, a new proof of existence and uniqueness results is proposed. The mass redistribution method, which is based on a redistribution of the body mass such that there is no inertia at the contact node, is introduced and its convergence is proved. Finally, some numerical experiments are reported.
Entropy regularization of the transonic potential flow problem
Miloslav Feistauer, Jan Mandel, Jindřich Nečas (1984)
Commentationes Mathematicae Universitatis Carolinae
Existence et unicité de solutions pour une inéquation de type hyperbolique du second ordre non linéaire
Brahim Hajouj (2001)
Annales mathématiques Blaise Pascal
Existence of solutions for a variational unilateral system.
Clark, Marcondes R., Lima, Osmundo A. (2002)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint
Florent Berthelin (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.
Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint
Florent Berthelin (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.
Obstacle problems for scalar conservation laws
Laurent Levi (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
In this paper we are interested in bilateral obstacle problems for quasilinear scalar conservation laws associated with Dirichlet boundary conditions. Firstly, we provide a suitable entropy formulation which ensures uniqueness. Then, we justify the existence of a solution through the method of penalization and by referring to the notion of entropy process solution due to specific properties of bounded sequences in . Lastly, we study the behaviour of this solution and its stability properties with...
Obstacle problems for scalar conservation laws
Laurent Levi (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
In this paper we are interested in bilateral obstacle problems for quasilinear scalar conservation laws associated with Dirichlet boundary conditions. Firstly, we provide a suitable entropy formulation which ensures uniqueness. Then, we justify the existence of a solution through the method of penalization and by referring to the notion of entropy process solution due to specific properties of bounded sequences in L∞. Lastly, we study the behaviour of this solution and its stability properties...
On a parabolic strongly nonlinear problem on manifolds.
Marinho, A.O., Louredo, A.T., Lima, O.A. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
On a variational inequality for the nonhomogeneous degenerated Kirchhoff equation with a frictional damping.
Frota, C.L., Lar'kin, N.A. (1998)
Portugaliae Mathematica
On asymptotic behavior of global solutions for hyperbolic hemivariational inequalities.
Park, Jong Yeoul, Park, Sun Hye (2006)
Electronic Journal of Differential Equations (EJDE) [electronic only]
On some variational inequalities for nonclassical type operators
Sergey Glazatov (1992)
Banach Center Publications
The purpose of this paper is to make a brief review of results obtained in the theory of variational inequalities for nonclassical operators, namely, of degenerate hyperbolic and variable type.
Optimal design problems for a dynamic viscoelastic plate. I. Short memory material
Igor Bock (1995)
Applications of Mathematics
We deal with an optimal control problem with respect to a variable thickness for a dynamic viscoelastic plate with velocity constraints. The state problem has the form of a pseudohyperbolic variational inequality. The existence and uniqueness theorem for the state problem and the existence of an optimal thickness function are proved.
Problèmes unilatéraux pour des équations non linéaires de convection-réaction
Laurent Lévi (1995)
Annales de la Faculté des sciences de Toulouse : Mathématiques
Remark to dynamic contact problems for bodies with a singular memory
Jiří Jarušek (1998)
Commentationes Mathematicae Universitatis Carolinae
The existence of a solution to the dynamic contact of a body having a singular memory with a rigid undeformable support is proved under some weaker assumption than that in [3].
Currently displaying 1 – 20 of 34
Page 1 Next