Work

Mild solutions to fourth-order parabolic equations modeling thin film growth with time fractional derivative

Year: 2024

Type: article

Abstract: In this article, we study initial-boundary problems for fourth-order nonlinear parabolic equations modeling thin film growth with Caputo-type time fractional derivative. By means of the theory of abstract fractional calculus and \(L^p-L^q\) estimates, we establish the existence and uniqueness of local mild solutions in the spaces \(C([0,T]; L^{\frac{\beta N}{2-\beta}}(\Omega))\) with \(1<\beta<2\). Moreover, the local solutions can be extended globally if the initial data is sufficiently small. For more information see https://ejde.math.txstate.edu/Volumes/2024/58/abstr.html

Source: Electronic Journal of Differential Equations

DOI: 10.58997/ejde.2024.58

Authors: Qiang Liu, Wanyu Zhu, Hailong Ye

Institution: Shenzhen University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, China Scholarship Council, Basic and Applied Basic Research Foundation of Guangdong Province

Awards: G3093013203, G4044603684, G4721959517, G7541410044