scholarly journals Classical solutions to quasilinear parabolic problems with dynamic boundary conditions

2016 ◽  
Vol 9 (3) ◽  
pp. 717-736
Author(s):  
Davide Guidetti
Keyword(s):  
Boundary Conditions ◽  
Parabolic Problems ◽  
Classical Solutions ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary ◽  
Quasilinear Parabolic Problems ◽  
Quasilinear Parabolic

scholarly journals Blow-Up Solutions and Global Existence for Quasilinear Parabolic Problems with Robin Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Juntang Ding
Keyword(s):  
Boundary Conditions ◽  
Global Solution ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Parabolic Problems ◽  
Robin Boundary Conditions ◽  
Quasilinear Parabolic Problems ◽  
Robin Boundary ◽  
Upper Estimate ◽  
Quasilinear Parabolic

We study the blow-up and global solutions for a class of quasilinear parabolic problems with Robin boundary conditions. By constructing auxiliary functions and using maximum principles, the sufficient conditions for the existence of blow-up solution, an upper bound for the “blow-up time,” an upper estimate of the “blow-up rate,” the sufficient conditions for the existence of global solution, and an upper estimate of the global solution are specified.

scholarly journals Higher-order exponential integrators for constrained semi-linear parabolic problems

2020 ◽  
Vol 2 (1) ◽  
pp. 14-20
Author(s):  
Johannes Wiedemann
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Dynamic ◽  
Order Of Convergence ◽  
Parabolic Systems ◽  
Higher Order ◽  
Parabolic Problems ◽  
Dynamic Boundary Conditions ◽  
Exponential Integrators ◽  
Dynamic Boundary

This paper provides an introduction to exponential integrators for constrained parabolic systems. In addition, building on existing results, schemes with an expected order of convergence of three and four are established and numerically tested on parabolic problems with nonlinear dynamic boundary conditions. The simulations reinforce the subjected error behaviour.

Monotone Finite Difference Schemes for Quasilinear Parabolic Problems with Mixed Boundary Conditions

2016 ◽  
Vol 16 (2) ◽  
pp. 231-243
Author(s):  
Francisco José Gaspar ◽  
Francisco Javier Lisbona ◽  
Piotr P. Matus ◽  
Vo Thi Kim Tuyen
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Finite Difference Methods ◽  
Neumann Boundary ◽  
Numerical Approach ◽  
Parabolic Problems ◽  
Finite Difference Schemes ◽  
Quasilinear Parabolic Problems ◽  
Quasilinear Parabolic

AbstractIn this paper, we consider finite difference methods for two-dimensional quasilinear parabolic problems with mixed Dirichlet–Neumann boundary conditions. Some strong two-side estimates for the difference solution are provided and convergence results in the discrete norm are proved. Numerical examples illustrate the good performance of the proposed numerical approach.

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