Semilinear wave equations with angularly smooth data
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Michael Beals (1984)
Journées équations aux dérivées partielles
Richard B. Melrose (1987)
Journées équations aux dérivées partielles
Jürgen Gärtner, Errico Presutti (1990)
Annales de l'I.H.P. Physique théorique
Razani, Abdolrahman (2007)
Surveys in Mathematics and its Applications
T. Gramchev, L. Cadeddu (1998)
Monatshefte für Mathematik
V. M. Shelkovich* (2010)
Banach Center Publications
We discuss the definitions of singular solutions (in the form of integral identities) to systems of conservation laws such as shocks, δ-, δ’-, and -shocks (n = 2,3,...). Using these definitions, the Rankine-Hugoniot conditions for δ- and δ’-shocks are derived. The weak asymptotics method for the solution of the Cauchy problems admitting δ- and δ’-shocks is briefly described. The algebraic aspects of such singular solutions are studied. Namely, explicit formulas for flux-functions of singular solutions...
Saxton, R., Vinod, V. (1995)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Denis Serre (1998)
Annales de l'institut Fourier
Nous considérons ici des solutions particulières des systèmes paraboliques de lois de conservation dans le domaine ou bien pour :Nous faisons l’hypothèse que le système réduit est hyperbolique. Notre but est la description de l’interaction d’ondes simples, mono-dimensionnelles, le plus souvent deux ondes exactement. L’une d’elle, au moins, est une onde de choc (pour le système réduit) visqueuse (pour le système parabolique). Il y a donc a priori un champ caractéristique vraiment non linéaire....
Alberto Strumia (1983)
Annales de l'I.H.P. Physique théorique
G. Métivier (1988/1989)
Séminaire Équations aux dérivées partielles (Polytechnique)
Denis Serre (1998/1999)
Séminaire Équations aux dérivées partielles
A powerfull method has been developped in [2] for the study of -stability of travelling waves in conservation laws or more generally in equations which display -contractivity, maximum principle and mass conservation. We recall shortly the general procedure. We also show that it partly applies to the waves of a model of radiating gas. These waves have first been studied by Kawashima and Nishibata [5,6] in a different framework. Therefore, shock fronts for this model are stable under mild perturbations....
Andrea Corli, Monique Sablé-Tougeron (1997)
Rendiconti del Seminario Matematico della Università di Padova
Nicola, Aurelian (2005)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
Massimiliano Daniele Rosini (2005)
Archivum Mathematicum
In this paper we study the stability of transonic strong shock solutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construction of a pseudo-local symmetrizer and on the paradifferential calculus with parameters, which combines the work of Bony-Meyer and the introduction of a large parameter.
Camillo De Lellis, Felix Otto (2003)
Journal of the European Mathematical Society
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