Math. Model. Nat. Phenom.
Volume 11, Number 2, 2016Spectral problems
|Page(s)||89 - 99|
|Published online||21 March 2016|
On the Well-posedness of Some generalized Characteristic Cauchy Problems
1 Laboratoire CEREGMIA, Université des
Antilles, Campus de
BP 7209, 97275
2 Laboratoire CRREF, IUFM de Guadeloupe, Morne Ferret, BP 399, 97178 Abymes Cedex, Guadeloupe
3 Department of Mathematics, Ghent University, Building S22, Krijgslaan 281, B 9000 Gent, Belgium
⋆ Corresponding author. E-mail: firstname.lastname@example.org
By means of convenient regularization for an ill posed Cauchy problem, we define an associated generalized problem and discuss the conditions for the solvability of it. To illustrate this, starting from the semilinear unidirectional wave equation with data given on a characteristic curve, we show existence and uniqueness of the solution.
Mathematics Subject Classification: 35A01 / 35A02 / 35A25 / 35D99 / 46F30 / 46T30
Key words: regularization of data / regularization of data / regularisation of problems / distributions / nonlinear generalized functions / / nonlinear problems / characteristic problems / transport equation
© EDP Sciences, 2016
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