Cauchy problem for a class of fourth-order semilinear pseudohyperbolic equations with structural damping

被引：1
|
作者：
Aliev, A. B. [1 ,2 ]
Pashayev, A. F. [2 ]
机构：
[1] Azerbaijan Tech Univ, AZ-1073 Baku, Azerbaijan
[2] Natl Acad Sci Azerbaijan, Inst Math & Mech, AZ-1141 Baku, Azerbaijan
来源：
DOKLADY MATHEMATICS | 2015年 / 92卷 / 03期
关键词：
PSEUDO-HYPERBOLIC EQUATIONS;
D O I：
10.1134/S1064562415060010
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A sufficient condition for the existence of global solutions is established, and the rate of decay of solutions to the Cauchy problem for a semilinear pseudohyperbolic equation with structural damping is found. The nonexistence of global solutions is also investigated. An analogue of the critical Fujita exponent is obtained for the considered problem.
引用
收藏
页码：651 / 654
页数：4
相关论文
共 50 条
  • [1] Cauchy problem for a class of fourth-order semilinear pseudohyperbolic equations with structural damping
    A. B. Aliev
    A. F. Pashayev
    [J]. Doklady Mathematics, 2015, 92 : 651 - 654
  • [2] EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTION OF CAUCHY PROBLEM FOR A CLASS OF SYSTEM OF SEMILINEAR HYPERBOLIC EQUATIONS OF FOURTH ORDER WITH DAMPING
    Aliev, Akbar B.
    Guliyeva, Vusala F.
    [J]. PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2014, 40 (01): : 80 - 92
  • [3] On the Cauchy problem of fourth-order nonlinear Schrodinger equations
    Guo, Ai
    Cui, Shangbin
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 66 (12) : 2911 - 2930
  • [4] On the Cauchy problem for a class of semilinear second order evolution equations with fractional Laplacian and damping
    Fujiwara, Kazumasa
    Ikeda, Masahiro
    Wakasugi, Yuta
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2021, 28 (06):
  • [5] Existence of the global solutions of the Cauchy problem for a system of semilinear pseudohyperbolic equations with structural dissipation
    Aliev, A. B.
    Pashaev, A. F.
    [J]. MATHEMATICAL NOTES, 2017, 101 (5-6) : 1050 - 1052
  • [6] On the Cauchy problem for a class of semilinear second order evolution equations with fractional Laplacian and damping
    Kazumasa Fujiwara
    Masahiro Ikeda
    Yuta Wakasugi
    [J]. Nonlinear Differential Equations and Applications NoDEA, 2021, 28
  • [7] Existence of the global solutions of the Cauchy problem for a system of semilinear pseudohyperbolic equations with structural dissipation
    A. B. Aliev
    A. F. Pashaev
    [J]. Mathematical Notes, 2017, 101 : 1050 - 1052
  • [8] Cauchy problem for some fourth-order nonstrictly hyperbolic equations
    Korzyuk, V. I.
    Vinh, N. V.
    [J]. NANOSYSTEMS-PHYSICS CHEMISTRY MATHEMATICS, 2016, 7 (05): : 869 - 879
  • [9] Entire Solutions for a Class of Fourth-Order Semilinear Elliptic Equations with Weights
    Paolo Caldiroli
    Gabriele Cora
    [J]. Mediterranean Journal of Mathematics, 2016, 13 : 657 - 675
  • [10] On the Cauchy Problem for Pseudohyperbolic Equations with Lower Order Terms
    Bondar, Lina N.
    Demidenko, Gennadii V.
    [J]. MATHEMATICS, 2023, 11 (18)
12345