caa a22 4500 475797299 CHVBK 20180406123728.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1007/PL00001519 doi (NATIONALLICENCE)springer-10.1007/PL00001519 Energy estimates and uniqueness of the weak solutions of initial-boundary value problems for semilinear hyperbolic systems [Elektronische Daten] [C. Făciu, N. Simion] Abstract.: Bounds in energy for the smooth solutions of initial and boundary value problems for semilinear hyperbolic systems are given. We prove that the integral energy identities for smooth solutions are still valid for weak solutions (i.e., piecewise continuous and piecewise continuously differentiable solutions separated by shock and/or acceleration waves). Energy estimates of the weak solutions of the same problems are given. The way weak and strong discontinuities in the input data affect the regularity of the total energy of the solutions is discussed. The uniqueness in L 2 sense of the weak solutions is derived. Birkhäuser Verlag, Basel,, 2000 Key words. Semilinear hyperbolic systems, weak solutions, shock waves, acceleration waves, jump relations, energy inequalities nationallicence Făciu C. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700, Bucharest, Romania, e-mail: cfaciu@stoilow.imar.ro, RO aut Simion N. Department of Mathematics, Technical University of Civil Engineering of Bucharest, Bd. Lacul Tei 124, RO-72302, Bucharest, Romania, RO aut https://doi.org/10.1007/PL00001519 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00001519 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Făciu C. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700, Bucharest, Romania, e-mail: cfaciu@stoilow.imar.ro, RO aut NATIONALLICENCE 700 1- Simion N. Department of Mathematics, Technical University of Civil Engineering of Bucharest, Bd. Lacul Tei 124, RO-72302, Bucharest, Romania, RO aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer