Existence and blow up of solutions for m ( x )- biharmonic equation with variable exponent sources

被引：0
作者：
Butakin, Gulistan [1 ]
Pis, Erhan [2 ]
机构：
[1] Dicle Univ, Inst Nat & Appl Sci, Diyarbakir, Turkiye
[2] Dicle Univ, Dept Math, Diyarbakir, Turkiye
来源：
FILOMAT | 2024年 / 38卷 / 22期
关键词：
m(x)- Biharmonic equation; energy; existence; global existence; Sobolev spaces; variable exponent; 4TH-ORDER PARABOLIC EQUATION; TIME; GROWTH; ENERGY; SYSTEM; BOUNDS; MODEL;
D O I：
10.2298/FIL2422871B
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work concerned with the existence and blow up of solutions for m (x) - biharmonic equation with variable exponent sources. Under appropriate conditions, we discuss the stationary problem and potential wells. By using the Faedo-Galerkin method, we prove the global existence of the solution. We also investigate the blow up of solutions with negative initial energy.
引用
收藏
页码：7871 / 7893
页数：23
相关论文
共 38 条
  • [11] Existence of solutions for a p(x)-Kirchhoff-type equation
    Dai, Guowei
    Hao, Ruifang
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 359 (01) : 275 - 284
  • [12] Lebesgue and Sobolev Spaces with Variable Exponents
    Diening, Lars
    Harjulehto, Petteri
    Hasto, Peter
    Ruzicka, Michael
    [J]. LEBESGUE AND SOBOLEV SPACES WITH VARIABLE EXPONENTS, 2011, 2017 : 1 - +
  • [13] UPPER BOUNDS FOR THE BLOW UP TIME FOR THE KIRCHHOFF-TYPE EQUATION
    Dinc, Yavuz
    Piskin, Erhan
    Tunc, Cemil
    [J]. COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2023, 72 (02): : 352 - 362
  • [14] Existence and Asymptotic Behavior of Beam-Equation Solutions with Strong Damping and p(x)-Biharmonic Operator
    Ferreira, Jorge
    Panni, Willian S.
    Messaoudi, Salim A.
    Piskin, Erhan
    Shahrouzi, Mohammad
    [J]. JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY, 2022, 18 (04) : 488 - 513
  • [15] Gazzola F, 2005, DIFFER INTEGRAL EQU, V18, P961
  • [16] A class of fourth-order parabolic equation with arbitrary initial energy
    Han, Yuzhu
    [J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2018, 43 : 451 - 466
  • [17] EXISTENCE AND BLOW-UP OF SOLUTIONS TO A PARABOLIC EQUATION WITH NONSTANDARD GROWTH CONDITIONS
    Liu, Yang
    [J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2019, 99 (02) : 242 - 249
  • [18] Elliptic Kirchhoff-type system with two convections terms and under Dirichlet boundary conditions
    Moujane, Noureddine
    El Ouaarabi, Mohamed
    Allalou, Chakir
    [J]. FILOMAT, 2023, 37 (28) : 9693 - 9707
  • [19] A continuum model of kinetic roughening and coarsening in thin films
    Ortiz, M
    Repetto, EA
    Si, H
    [J]. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 1999, 47 (04) : 697 - 730
  • [20] SADDLE POINTS AND INSTABILITY OF NONLINEAR HYPERBOLIC EQUATIONS
    PAYNE, LE
    SATTINGER, DH
    [J]. ISRAEL JOURNAL OF MATHEMATICS, 1975, 22 (3-4) : 273 - 303
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