an:04190248
Zbl 0722.35025
Tsuji, Mikio
Prolongation of classical solutions and singularities of generalized solutions
EN
Ann. Inst. Henri Poincar??, Anal. Non Lin??aire 7, No. 6, 505-523 (1990).
00156099
1990
j
35F25 35L67 35B65
global classical solutions; formation of singularities; Cauchy problems; Rankin-Hugoniot's condition
Conditions for existence of global classical solutions or formation of singularities in solutions of Cauchy problems for general partial differential equations of first order are obtained. The reason why properties of singularities may depend on the type of equations (Hamilton-Jacobi equations, conservation laws) is discussed. The Rankin- Hugoniot's condition for a single quasilinear equation is solved.
L.G.Vulkov (Russe)