Existence and decay of finite energy solutions for semilinear dissipative wave equations in time-dependent domains

• Autorzy: Nakao Mitsuhiro

Identyfikatory

DOI

10.7494/OpMath.2020.40.6.725

• Języki publikacji: EN

Abstrakty

EN

We consider the initial-boundary value problem for semilinear dissipative wave equations in noncylindrical domain [formula]. We are interested in finite energy solution. We derive an exponential decay of the energy in the case Ω (t) is bounded in [formula] and the estimate [formula] in the case Ω (t) is unbounded. Existence and uniqueness of finite energy solution are also proved.

Słowa kluczowe

EN

energy decay; global existence; semilinear wave equation; noncylindrical domains

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2020
• Tom: Vol. 40, no. 6
• Strony: 725--736
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Nakao Mitsuhiro

• Faculty of Mathematics Kyushu University Moto-oka 744, Fukuoka 819-0395, Japan

Bibliografia

• [1] J. Cooper, Local decay of solutions of the wave equation in the exterior of a moving body, J. Math. Anal. Appl. 49 (1975), 130-153.
• [2] M. Ikawa, Mixed problems for hyperbolic equations of second order, J. Math. Soc. Japan 20 (1968), 580-608.
• [3] A. Inoue, Sur □ u + u3 = f dans un domaine noncylindrique, J. Math. Anal. Appl. 46 (1974), 777-819.
• [4] O. Ladyzhenskaya, On the solution of some non-stationary operator equations, Math. Sb. 39 (1961), 441-524 [in Russian].
• [5] K. Lee, A mixed problem for hyperbolic equations with time-depenent domain, J. Math. Anal. Appl. 16 (1966), 455-471.
• [6] M. Nakao, Periodic solution of the dissipative wave equation in a time-dependent domain, J. Differential Equations 34 (1979), 393-404.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020)