The authors of this paper study the Bresse system in bounded domain with delay terms.First,we prove the global existence of its solutions in Sobolev spaces by means of semigroup theory.Furthermore,the asymptotic stabi...The authors of this paper study the Bresse system in bounded domain with delay terms.First,we prove the global existence of its solutions in Sobolev spaces by means of semigroup theory.Furthermore,the asymptotic stability is given by using an appropriate Lyapunov functional.展开更多
We are interested in the study of a coupled system of viscoelastic wave equa- tions with a delay term. Firstly global existence of the solutions is proved. The asymp- totic behavior is obtained by using multiplier tec...We are interested in the study of a coupled system of viscoelastic wave equa- tions with a delay term. Firstly global existence of the solutions is proved. The asymp- totic behavior is obtained by using multiplier technique proved by A. Guessmia [1], however in the unstable set for certain initial data bolstered with some conditions, we obtain the blow up of the solutions for various sign of initial energy negative, positive or null. We use the same technique in [2] with a necessary modification imposed by our problem. This improves the earlier results in the literature展开更多
We considered the Cauchy problem for the fractional wave-diffusion equation D^αu-△｜u｜^m-1u＋（-△）^β/2D^γ｜u｜^l-1u=h（x,t）｜u｜^p＋f（x,t）with given initial data and where p〉1,1〈α〈2,0〈β〈2,0〈γ〈1.Non...We considered the Cauchy problem for the fractional wave-diffusion equation D^αu-△｜u｜^m-1u＋（-△）^β/2D^γ｜u｜^l-1u=h（x,t）｜u｜^p＋f（x,t）with given initial data and where p〉1,1〈α〈2,0〈β〈2,0〈γ〈1.Nonexistence results and necessary conditions for global existence are established by means of th, test function method. This results extend previous works.展开更多
文摘The authors of this paper study the Bresse system in bounded domain with delay terms.First,we prove the global existence of its solutions in Sobolev spaces by means of semigroup theory.Furthermore,the asymptotic stability is given by using an appropriate Lyapunov functional.
文摘We are interested in the study of a coupled system of viscoelastic wave equa- tions with a delay term. Firstly global existence of the solutions is proved. The asymp- totic behavior is obtained by using multiplier technique proved by A. Guessmia [1], however in the unstable set for certain initial data bolstered with some conditions, we obtain the blow up of the solutions for various sign of initial energy negative, positive or null. We use the same technique in [2] with a necessary modification imposed by our problem. This improves the earlier results in the literature
文摘We considered the Cauchy problem for the fractional wave-diffusion equation D^αu-△｜u｜^m-1u＋（-△）^β/2D^γ｜u｜^l-1u=h（x,t）｜u｜^p＋f（x,t）with given initial data and where p〉1,1〈α〈2,0〈β〈2,0〈γ〈1.Nonexistence results and necessary conditions for global existence are established by means of th, test function method. This results extend previous works.
