scholarly journals General decay and blow‐up results for a nonlinear pseudoparabolic equation with Robin–Dirichlet conditions

2021 ◽  
Author(s):  
Le Thi Phuong Ngoc ◽  
Nguyen Huu Nhan ◽  
Nguyen Thanh Long
Keyword(s):  
Blow Up ◽  
General Decay ◽  
Pseudoparabolic Equation ◽  
Dirichlet Conditions ◽  
Nonlinear Pseudoparabolic Equation

scholarly journals Blow-Up of Solutions for a Class of Nonlinear Pseudoparabolic Equations with a Memory Term

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Huafei Di ◽  
Yadong Shang
Keyword(s):  
Boundary Condition ◽  
Relaxation Function ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Initial Energy ◽  
Memory Term ◽  
Initial Condition ◽  
Pseudoparabolic Equation ◽  
Pseudoparabolic Equations ◽  
Nonlinear Pseudoparabolic Equation

We consider the nonlinear pseudoparabolic equation with a memory termut-Δu-Δut+∫0tλt-τΔuτdτ=div∇up-2u+u1+α,x∈Ω,t>0, with an initial condition and Dirichlet boundary condition. Under negative initial energy and suitable conditions onp,α, and the relaxation functionλ(t), we prove a finite-time blow-up result by using the concavity method.

scholarly journals General Decay Rate of Solution for Love-Equation with Past History and Absorption

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1632
Author(s):  
Khaled Zennir ◽  
Mohamad Biomy
Keyword(s):  
Decay Rate ◽  
Source Term ◽  
Blow Up ◽  
Past History ◽  
Point Of View ◽  
General Decay ◽  
General Decay Rate ◽  
Infinite Memory ◽  
New Class ◽  
The Relationship

In the present paper, we consider an important problem from the point of view of application in sciences and engineering, namely, a new class of nonlinear Love-equation with infinite memory in the presence of source term that takes general nonlinearity form. New minimal conditions on the relaxation function and the relationship between the weights of source term are used to show a very general decay rate for solution by certain properties of convex functions combined with some estimates. Investigations on the propagation of surface waves of Love-type have been made by many authors in different models and many attempts to solve Love’s equation have been performed, in view of its wide applicability. To our knowledge, there are no decay results for damped equations of Love waves or Love type waves. However, the existence of solution or blow up results, with different boundary conditions, have been extensively studied by many authors. Our interest in this paper arose in the first place in consequence of a query for a new decay rate, which is related to those for infinite memory ϖ in the third section. We found that the system energy decreased according to a very general rate that includes all previous results.

scholarly journals On the nonlinear pseudoparabolic equation with the mixed inhomogeneous condition

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Le Thi Phuong Ngoc ◽  
Truong Thi Nhan ◽  
Tran Minh Thuyet ◽  
Nguyen Thanh Long
Keyword(s):  
Pseudoparabolic Equation ◽  
Inhomogeneous Condition ◽  
Nonlinear Pseudoparabolic Equation

scholarly journals Existence, blow-up and exponential decay estimates for the nonlinear Kirchhoff-Carrier wave equation in an annular with nonhomogeneous Dirichlet conditions

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5561-5588 ◽  
Author(s):  
le Son ◽  
Le Ngoc ◽  
Nguyen Long
Keyword(s):  
Wave Equation ◽  
Exponential Decay ◽  
Existence And Uniqueness ◽  
Lyapunov Functional ◽  
Blow Up ◽  
Initial Energy ◽  
Decay Estimates ◽  
Carrier Wave ◽  
Dirichlet Conditions ◽  
Uniqueness Of The Solution

This paper is devoted to the study of a nonlinear Kirchhoff-Carrier wave equation in an annular associated with nonhomogeneous Dirichlet conditions. At first, by applying the Faedo-Galerkin, we prove existence and uniqueness of the solution of the problem considered. Next, by constructing Lyapunov functional, we prove a blow-up result for solutions with a negative initial energy and establish a sufficient condition to obtain the exponential decay of weak solutions.

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