scholarly journals Existence, blow-up and exponential decay estimates for a system of nonlinear viscoelastic wave equations with nonlinear boundary conditions

2020 ◽  
Vol 19 (1) ◽  
pp. 455-492 ◽  
Author(s):  
Nguyen Thanh Long ◽  
◽  
Hoang Hai Ha ◽  
Le Thi Phuong Ngoc ◽  
Nguyen Anh Triet ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Exponential Decay ◽  
Wave Equations ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Nonlinear Boundary Conditions ◽  
Decay Estimates ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Wave

scholarly journals Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions

2008 ◽  
Vol 2008 ◽  
pp. 1-29 ◽  
Author(s):  
Louis A. Assalé ◽  
Théodore K. Boni ◽  
Diabate Nabongo
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Analogous Result ◽  
Nonlinear Boundary Conditions ◽  
Semilinear Parabolic Equation ◽  
Discrete Form ◽  
Semilinear Equation ◽  
Blow Up Rate ◽  
Semilinear Parabolic

We obtain some conditions under which the positive solution for semidiscretizations of the semilinear equationut=uxx−a(x,t)f(u),  0<x<1,  t∈(0,T), with boundary conditionsux(0,t)=0,ux(1,t)=b(t)g(u(1,t)), blows up in a finite time and estimate its semidiscrete blow-up time. We also establish the convergence of the semidiscrete blow-up time and obtain some results about numerical blow-up rate and set. Finally, we get an analogous result taking a discrete form of the above problem and give some computational results to illustrate some points of our analysis.

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