Existence and Uniqueness of Weak Solutions to a Thin Film Type Equation

2015 ◽  
Vol 738-739 ◽  
pp. 465-468
Author(s):  
Bo Liang ◽  
Hui Ying Shen ◽  
Xi Ting Peng ◽  
Mei Shan Wang
Keyword(s):  
Thin Film ◽  
Boundary Condition ◽  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Initial Function ◽  
Type Equation ◽  
Multidimensional Space ◽  
Discrete Problem ◽  
Uniqueness Of Solutions ◽  
Fourth Order Parabolic Equation

This paper is concerned with a fourth order parabolic equation in multidimensional spacewith boundary condition u=Δu=0 and initial function u0. The minimizer method yields the existence and uniqueness for the elliptic equation. Finally, the existence and uniqueness of solutions of the corresponding parabolic equation are obtained from the semi-discrete problem.

scholarly journals A fourth-order parabolic equation with a logarithmic nonlinearlity

2004 ◽  
Vol 69 (1) ◽  
pp. 35-48 ◽  
Author(s):  
Ahmed Bonfoh
Keyword(s):  
Free Energy ◽  
Parabolic Equation ◽  
Fourth Order ◽  
Constitutive Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Hilliard Equation ◽  
Finite Dimensional ◽  
Fourth Order Parabolic Equation ◽  
Cahn Hilliard Equation

We consider some generalisations of the Cahn—Hilliard equation based on constitutive equations derived by M. Gurtin in (1996) with a logarithmic free energy. Compared to the classical Cahn—Hilliard equation (see [4, 5]), these models take into account the work of internal microforces and the anisotropy of the material. We obtain the existence and uniqueness of solutions results and then prove the existence of finite dimensional attractors.

On the solutions of a fourth order parabolic equation modeling epitaxial thin film growth

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Ning Duan ◽  
Xiaopeng Zhao ◽  
Xiufang Zhao
Keyword(s):  
Thin Film ◽  
Parabolic Equation ◽  
Fourth Order ◽  
Film Growth ◽  
Thin Film Growth ◽  
Equation Modeling ◽  
Epitaxial Thin Film ◽  
Epitaxial Thin Film Growth ◽  
Order Parabolic Equation ◽  
Fourth Order Parabolic Equation

AbstractIn this paper, we study the existence and uniqueness of global weak solution, the regularity of the solutions and the existence of global attractor for a fourth order parabolic equation modeling epitaxial thin film growth with Neumann boundary conditions in two space dimensions.

scholarly journals On an analogue of the Tricomi problem for a «pointwise» loaded hyperbolic-parabolic equation

2021 ◽  
pp. 29-39
Author(s):  
К.У. Хубиев
Keyword(s):  
Parabolic Equation ◽  
Fixed Points ◽  
Unique Solvability ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Tricomi Problem ◽  
Uniqueness Of Solutions

Для нагруженного уравнения гиперболо-параболического типа исследуется однозначная разрешимость аналога задача Трикоми. Нагрузка определена в фиксированных точках области искомых решений, в том числе и во внутренних точках. Найдены условия существования и единственности регулярного решения задачи. The unique solvability of an analogue of the Tricomi problem is investigated for a loaded hyperbolic-parabolic equation. The load is determined at boundary and interior fixed points of the domain in which the solutions are sought. Sufficient conditions are found for the existence and uniqueness of solutions.

Elliptic-Parabolic Equation with Absorption of Obstacle type

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Noureddine Igbida ◽  
Fahd Karami
Keyword(s):  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Parabolic Problem ◽  
Uniqueness Of Solutions ◽  
Degenerate Parabolic Problem ◽  
Doubly Nonlinear ◽  
Degenerate Parabolic ◽  
Nonlinear Degenerate

AbstractThis paper is concerned with existence and uniqueness of solutions for a doubly nonlinear degenerate parabolic problem of the type β(w)

scholarly journals Asymptotic behavior of solutions for a semibounded nonmonotone evolution equation

2003 ◽  
Vol 2003 (9) ◽  
pp. 521-538
Author(s):  
Nikos Karachalios ◽  
Nikos Stavrakakis ◽  
Pavlos Xanthopoulos
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Parabolic Equation ◽  
Evolution Equation ◽  
Existence And Uniqueness ◽  
Nonlinear Parabolic Equation ◽  
Evolution Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Nonlinear Parabolic

We consider a nonlinear parabolic equation involving nonmonotone diffusion. Existence and uniqueness of solutions are obtained, employing methods for semibounded evolution equations. Also shown is the existence of a global attractor for the corresponding dynamical system.

Sign in / Sign up

Export Citation Format

Share Document