Global existence, nonexistence, and decay of solutions for a wave equation of p-Laplacian type with weak and p-Laplacian damping, nonlinear boundary delay and source terms

2021 ◽  
pp. 1-16
Author(s):  
Nouri Boumaza ◽  
Billel Gheraibia
Keyword(s):  
Global Existence ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Source Terms ◽  
Delay Term ◽  
Laplacian Equation ◽  
Decay Of Solutions

In this paper, we consider the initial boundary value problem for the p-Laplacian equation with weak and p-Laplacian damping terms, nonlinear boundary, delay and source terms acting on the boundary. By introducing suitable energy and perturbed Lyapunov functionals, we prove global existence, finite time blow up and asymptotic behavior of solutions in cases p > 2 and p = 2. To our best knowledge, there is no results of the p-Laplacian equation with a nonlinear boundary delay term.

scholarly journals Global Existence and Blow-Up for the Pseudo-parabolic p(x)-Laplacian Equation with Logarithmic Nonlinearity

2021 ◽  
Author(s):  
Fugeng Zeng ◽  
Qigang Deng ◽  
Dongxiu Wang
Keyword(s):  
Global Existence ◽  
Boundary Value Problem ◽  
Global Solution ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Potential Well ◽  
Laplacian Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the initial boundary value problem of the pseudo-parabolic p(x)-Laplacian equation with logarithmic nonlinearity. The existence of the global solution is obtained by using the potential well method and the logarithmic inequality. In addition, the sufficient conditions of the blow-up are obtained by concavity method.

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER–STOKES EQUATIONS FOR A 1D ISOTHERMAL VISCOUS GAS

2008 ◽  
Vol 18 (08) ◽  
pp. 1383-1408 ◽  
Author(s):  
YUMING QIN ◽  
YANLI ZHAO
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Stokes Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Navier Stokes Equations ◽  
Viscous Gas ◽  
Initial Boundary Value

In this paper, we prove the global existence and asymptotic behavior of solutions in Hi(i = 1, 2) to an initial boundary value problem of a 1D isentropic, isothermal and the compressible viscous gas with an non-autonomous external force in a bounded region.

scholarly journals Global Existence and Blow-Up for the Euler-Bernoulli Plate Equation with Variable Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Jianghao Hao ◽  
Jie Lan
Keyword(s):  
Global Existence ◽  
Blow Up ◽  
Local Existence ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Stability Of Solutions ◽  
Plate Equation ◽  
Existence And Stability ◽  
Initial Boundary Value

We prove the local existence, blow-up, global existence, and stability of solutions to the initial boundary value problem for Euler-Bernoulli plate equation with variable coefficients.

Existence and Blow-Up of Solutions for a Degenerate Semilinear Parabolic Equation

2013 ◽  
Vol 785-786 ◽  
pp. 1454-1458
Author(s):  
Yan Ping Ran ◽  
Cong Ming Peng
Keyword(s):  
Parabolic Equation ◽  
Global Existence ◽  
Boundary Value Problem ◽  
Blow Up ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Semilinear Parabolic Equation ◽  
Initial Boundary Value ◽  
Semilinear Parabolic

This article considers the following degenerate semilinear parabolic initial-boundary value problem,where be constants. We obtained the conditions of global existence and blow-up.

scholarly journals Blow up and asymptotic behavior of solutions for a p(x)-Laplacian equations with delay term and variadle exponents

2021 ◽  
Author(s):  
Stanilslav Antontsev ◽  
Jorge Ferreira ◽  
Erhan Pişkin ◽  
Hazal Yüksekkaya
Keyword(s):  
Asymptotic Behavior ◽  
Integral Inequality ◽  
Blow Up ◽  
Asymptotic Behavior Of Solutions ◽  
Variable Exponents ◽  
Delay Term ◽  
Laplacian Equation ◽  
Laplacian Equations ◽  
Equation With Delay ◽  
Equations With Delay

In this paper, we consider a nonlinear p .x/Laplacian equation with delay of time and variable exponents. Firstly, we prove the blow up of solutions. Then, by applying an integral inequality due to Komornik, we obtain the decay result. These results improve and extend earlier results in the literature.

scholarly journals Existence, Decay, and Blow-Up of Solutions for a Higher-Order Kirchhoff-Type Equation with Delay Term

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Hazal Yüksekkaya ◽  
Erhan Pişkin ◽  
Salah Mahmoud Boulaaras ◽  
Bahri Belkacem Cherif
Keyword(s):  
Blow Up ◽  
Type Equation ◽  
Initial Boundary ◽  
Initial Energy ◽  
Higher Order ◽  
Delay Term ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Decay Of Solutions ◽  
Equation With Delay

This article deals with the study of the higher-order Kirchhoff-type equation with delay term in a bounded domain with initial boundary conditions, where firstly, we prove the global existence result of the solution. Then, we discuss the decay of solutions by using Nakao’s technique and denote polynomially and exponentially. Furthermore, the blow-up result is established for negative initial energy under appropriate conditions.

A Class of Fourth Order Damped Wave Equations with Arbitrary Positive Initial Energy

2018 ◽  
Vol 62 (1) ◽  
pp. 165-178
Author(s):  
Yang Liu ◽  
Jia Mu ◽  
Yujuan Jiao
Keyword(s):  
Global Existence ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Wave Equations ◽  
Blow Up ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Energy ◽  
Positive Initial Energy ◽  
Initial Boundary Value

AbstractIn this paper, we study the initial boundary value problem for a class of fourth order damped wave equations with arbitrary positive initial energy. In the framework of the energy method, we further exploit the properties of the Nehari functional. Finally, the global existence and finite time blow-up of solutions are obtained.

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