nonlinear pseudoparabolic equation
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2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Nguyen Huu Nhan ◽  
Tran Trinh Manh Dung ◽  
Le Thi Mai Thanh ◽  
Le Thi Phuong Ngoc ◽  
Nguyen Thanh Long

In this paper, by applying the Faedo-Galerkin approximation method and using basic concepts of nonlinear analysis, we study the initial-boundary value problem for a nonlinear pseudoparabolic equation with Robin–Dirichlet conditions. It consists of two main parts. Part 1 is devoted to proof of the unique existence of a weak solution by establishing an approximate sequence u m based on a N -order iterative scheme in case of f ∈ C N 0,1 × 0 , T ∗ × ℝ N ≥ 2 , or a single-iterative scheme in case of f ∈ C 1 Ω ¯ × 0 , T ∗ × ℝ . In Part 2, we begin with the construction of a difference scheme to approximate u m of the N -order iterative scheme, with N = 2 . Next, we present numerical results in detail to show that the convergence rate of the 2-order iterative scheme is faster than that of the single-iterative scheme.


2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Le Thi Phuong Ngoc ◽  
Truong Thi Nhan ◽  
Tran Minh Thuyet ◽  
Nguyen Thanh Long

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Huafei Di ◽  
Yadong Shang

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.


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