On the Cauchy problem for the wave equation on time-dependent domains
One introduces a new concept for the solution of the wave equation on a time dependent domain and compare it with the one considered in a previous paper of the authors: [Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 22, No. 3, 387--408 (2011; Zbl 1239.35086)]. The new definition is based on integration by parts in time and does not require a precise definition of the value at time \(t\) of the second derivative of \(u(t)\). Under some special assumptions on initial data, an existence result for the solution to the Cauchy problem is proved. Additional conditions assure the uniqueness of solution.
scientific article; zbMATH DE number 7005197
scientific article