In this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the coefficient showing that dispersion occurs if this variation is small enough but it may fail when the variation goes beyond a sharp threshold. For the Schrödinger equation we prove that the dispersion holds under the same smallness assumption on the variation of the coefficient. But, whether dispersion may fail for larger coefficients is unknown for the Schrödinger equation.
@article{AIHPC_2016__33_6_1473_0, author = {Beli, Constantin N. and Ignat, Liviu I. and Zuazua, Enrique}, title = {Dispersion for {1-D} {Schr\"odinger} and wave equations with {BV} coefficients}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1473--1495}, publisher = {Elsevier}, volume = {33}, number = {6}, year = {2016}, doi = {10.1016/j.anihpc.2015.06.002}, zbl = {1364.35024}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2015.06.002/} }
TY - JOUR AU - Beli, Constantin N. AU - Ignat, Liviu I. AU - Zuazua, Enrique TI - Dispersion for 1-D Schrödinger and wave equations with BV coefficients JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 1473 EP - 1495 VL - 33 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2015.06.002/ DO - 10.1016/j.anihpc.2015.06.002 LA - en ID - AIHPC_2016__33_6_1473_0 ER -
%0 Journal Article %A Beli, Constantin N. %A Ignat, Liviu I. %A Zuazua, Enrique %T Dispersion for 1-D Schrödinger and wave equations with BV coefficients %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 1473-1495 %V 33 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2015.06.002/ %R 10.1016/j.anihpc.2015.06.002 %G en %F AIHPC_2016__33_6_1473_0
Beli, Constantin N.; Ignat, Liviu I.; Zuazua, Enrique. Dispersion for 1-D Schrödinger and wave equations with BV coefficients. Annales de l'I.H.P. Analyse non linéaire, Volume 33 (2016) no. 6, pp. 1473-1495. doi : 10.1016/j.anihpc.2015.06.002. http://www.numdam.org/articles/10.1016/j.anihpc.2015.06.002/
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