On the benefit of different additional regularity for the weakly coupled systems of semilinear effectively damped waves
The article refers to the classical Cauchy problem for a system of weakly coupled semilinear damped wave equations with time-dependent coefficients in the dissipation terms and power nonlinearities, with exponents \(p\) and \(q\). Under some assumptions on the exponents \(p\), \(q\), dissipation term coefficient and specific regularity conditions on data, one proves the existence of a uniquely determined globally -- in time -- Sobolev solution to the considered system, solution that satisfies certain decay estimates. In a special case, Sobolev solutions become energy solutions and additionally new estimates are proved. The two results in paper are similar and correspond to different choice of parameter.
scientific article; zbMATH DE number 6909954
scientific article