On uniqueness of weak solutions to semilinear wave equations
- 1 January 1982
- journal article
- research article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 7 (2) , 153-195
- https://doi.org/10.1080/03605308208820221
Abstract
Weak solutions to Cauchy problems of the form are considered for n≧3 , p > 1 . The data are assumed to be only of (locally) finite energy, and solutions u are to satisfy Uniqueness is obtained under any of the following three condition i) ii)solutions are radial and satisfy a certain well-known space-time estimate, and iii) for n = 3 and 1 < p < 5 , solutions which satisfy either an appropriate “cone estimate” or the abovementioned space-time estimate (due to Morawetz).Keywords
This publication has 6 references indexed in Scilit:
- On the existence of global smooth solutions of certain semi-linear hyperbolic equationsMathematische Zeitschrift, 1979
- OnL p?Lp? estimates for the wave-equationMathematische Zeitschrift, 1975
- Convolutions with kernels having singularities on a sphereTransactions of the American Mathematical Society, 1970
- Time decay for the nonlinear Klein-Gordon equationProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1968
- Non-Linear Semi-GroupsAnnals of Mathematics, 1963
- Das Anfangswertproblem in Gro en f r eine Klasse nichtlinearer WellengleichungenMathematische Zeitschrift, 1961