A refined description of evolving interfaces in certain nonlinear wave equations



We improve on recent results that establish the existence of solutions of certain semilinear wave equations possessing an interface that roughly sweeps out a timelike surface of vanishing mean curvature in Minkowski space. Compared to earlier work, we present sharper estimates, in stronger norms, of the solutions in question.


Semilinear wave equations Hyperbolic Interface Timelike hypersurface 

Mathematics Subject Classification

35L71 35B25 74N20 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsUniversity of New BrunswickFrederictonCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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