An asymmetric backward problem for the inhomogeneous parabolic equation with time-dependent diffusivity

2017 ◽  
Vol 37 (3) ◽  
pp. 3241-3255
Author(s):  
Triet Le Minh ◽  
Phong Luu Hong ◽  
Quan Pham Hoang
Keyword(s):  
Parabolic Equation ◽  
Time Dependent ◽  
Backward Problem

scholarly journals A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Pham Hoang Quan ◽  
Le Minh Triet ◽  
Dang Duc Trong
Keyword(s):  
Exact Solution ◽  
Parabolic Equation ◽  
Numerical Experiment ◽  
Time Dependent ◽  
Backward Problem ◽  
Nonlinear Parabolic ◽  
Boundary Value Method ◽  
Ill Posed ◽  
Sharp Error ◽  
Regularized Solution

We study the backward problem with time-dependent coefficient which is a severely ill-posed problem. We regularize this problem by combining quasi-boundary value method and quasi-reversibility method and then obtain sharp error estimate between the exact solution and the regularized solution. A numerical experiment is given in order to illustrate our results.

scholarly journals Doubly Degenerate Parabolic Equation with Time-Dependent Gradient Source and Initial Data Measures

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Lihua Deng ◽  
Xianguang Shang
Keyword(s):  
Parabolic Equation ◽  
Initial Data ◽  
Degenerate Parabolic Equation ◽  
A Priori Estimates ◽  
A Priori ◽  
Local Existence ◽  
Time Dependent ◽  
Priori Estimates ◽  
The Cauchy Problem ◽  
Degenerate Parabolic

This paper is devoted to the Cauchy problem for a class of doubly degenerate parabolic equation with time-dependent gradient source, where the initial data are Radon measures. Using the delicate a priori estimates, we first establish two local existence results. Furthermore, we show that the existence of solutions is optimal in the class considered here.

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