A Ritz-Galerkin approximation to the solution of parabolic equation with moving boundaries

DOI10.1186/s13661-015-0503-5zbMath1329.35364OpenAlexW2208013764WikidataQ59411410 ScholiaQ59411410MaRDI QIDQ903981

Jian-Rong Zhou, Heng Li

Publication date: 15 January 2016

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-015-0503-5

zbMATH Keywords

parabolic equationinitial boundary value problemmoving boundariesRitz-Galerkin methodBernstein polynomial basisapproximation solutionductal carcinoma in situ (DCIS) model

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Moving boundary problems for PDEs (35R37)

Related Items (4)

On a moving boundary problem associated with the swelling drug release platforms ⋮ Numerical algorithms for a free boundary problem model of DCIS and a related inverse problem ⋮ Another way of solving a free boundary problem related to DCIS model ⋮ Ritz–Galerkin method for solving an inverse problem of parabolic equation with moving boundaries and integral condition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Galerkin method applied to a parabolic evolution problem with nonlocal boundary conditions
• Curve offsetting based on Legendre series
• Determination of source parameter in parabolic equations
• Analysis of a mathematical model for the growth of tumors
• A free boundary problem model of ductal carcinoma in situ
• Legendre-Bernstein basis transformations
• Growth of necrotic tumors in the presence and absence of inhibitors
• Growth of nonnecrotic tumors in the presence and absence of inhibitors
• Solutions of differential equations in a Bernstein polynomial basis
• Some inverse problems raised from a mathematical model of ductal carcinoma in situ
• Parameter determination in a partial differential equation from the overspecified data
• A survey of models for tumor-immune system dynamics
• Application of the Ritz-Galerkin method for recovering the spacewise-coefficients in the wave equation
• Direct and inverse problem for the parabolic equation with initial value and time-dependent boundaries
• Ritz–Galerkin method for solving an inverse heat conduction problem with a nonlinear source term via Bernstein multi-scaling functions and cubic B-spline functions
• Ritz‐Galerkin method with Bernstein polynomial basis for finding the product solution form of heat equation with non‐classic boundary conditions
• Finding a control parameter in a one-dimensional parabolic inverse problem by using the Bernstein Galerkin method
• A free boundary problem of parabolic complex equation
• A free boundary problem of diffusion equation with integral condition
• Mathematical modelling of comedo ductal carcinoma in situ of the breast
• Models for the Growth of a Solid Tumor by Diffusion

This page was built for publication: A Ritz-Galerkin approximation to the solution of parabolic equation with moving boundaries