scholarly journals Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order

2020 ◽  
Author(s):  
Buyang Li ◽  
Hong Wang ◽  
Jilu Wang
Keyword(s):  
Numerical Solutions ◽  
Fractional Diffusion ◽  
Regularity Of Solutions ◽  
Implicit Time ◽  
Variable Order ◽  
Well Posedness ◽  
Rigorous Analysis ◽  
Time Stepping ◽  
Regularity Results ◽  
Unknown Solution

We prove well-posedness and regularity of solutions to a fractional diffusion porous media equation with a variable order that may depend on the unknown solution. We present a linearly implicit time-stepping method to linearize and discretize the equation in time, and present rigorous analysis for the convergence of numerical solutions based on proved regularity results.

scholarly journals Well-posedness and regularity results for a dynamic Von Kármán plate

1995 ◽  
Vol 18 (2) ◽  
pp. 237-244
Author(s):  
M. E. Bradley
Keyword(s):  
Strong Solutions ◽  
Free Edge ◽  
Regularity Of Solutions ◽  
Well Posedness ◽  
Boundary Damping ◽  
Von Karman ◽  
Edge Conditions ◽  
Von Kármán Plate ◽  
Regularity Results ◽  
Von Kármán

We consider the problem of well-posedness and regularity of solutions for a dynamic von Kármán plate which is clamped along one portion of the boundary and which experiences boundary damping through “free edge” conditions on the remainder of the boundary. We prove the existence of unique strong solutions for this system

NUMERICAL STUDIES OF CONJUGATED INFINITE ELEMENTS FOR ACOUSTICAL RADIATION

2000 ◽  
Vol 08 (01) ◽  
pp. 1-24 ◽  
Author(s):  
R. J. ASTLEY ◽  
J. A. HAMILTON
Keyword(s):  
Implicit Time ◽  
Variable Order ◽  
Shape Functions ◽  
Infinite Elements ◽  
Time Stepping ◽  
Oblate Spheroidal ◽  
Numerical Studies ◽  
Transient Solutions ◽  
Wave Problems ◽  
Spheroidal Coordinates

Aspects of conjugated infinite element schemes for unbounded wave problems are reviewed and a general formulation is presented for elements of variable order based on separable shape functions expressed in terms of prolate and oblate spheroidal coordinates. The formulation encompasses both "conjugated Burnett" and "Astley–Leis" elements. The performance of the two approaches is compared for steady multipole wave fields and the effect of the radial basis on the condition number of the resulting equations is discussed. Transient formulations based on these elements are derived and methods for solving the resulting transient equations are discussed. The use of an implicit time stepping scheme coupled with an indirect iterative solver is shown to give fast transient solutions which do not require matrix inversion.

scholarly journals On a time fractional diffusion with nonlocal in time conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nguyen Hoang Tuan ◽  
Nguyen Anh Triet ◽  
Nguyen Hoang Luc ◽  
Nguyen Duc Phuong
Keyword(s):  
Fourier Series ◽  
Diffusion Equation ◽  
Convergence Rate ◽  
Exact Solutions ◽  
Mild Solution ◽  
Integral Condition ◽  
Fractional Diffusion ◽  
Well Posedness ◽  
Nonlocal Integral Condition ◽  
Regularized Solution

AbstractIn this work, we consider a fractional diffusion equation with nonlocal integral condition. We give a form of the mild solution under the expression of Fourier series which contains some Mittag-Leffler functions. We present two new results. Firstly, we show the well-posedness and regularity for our problem. Secondly, we show the ill-posedness of our problem in the sense of Hadamard. Using the Fourier truncation method, we construct a regularized solution and present the convergence rate between the regularized and exact solutions.

Sign in / Sign up

Export Citation Format

Share Document