Global Weak Solutions to an Initial-Boundary Value Problem for a Three-phase Field Model of Solidification
نویسندگان
چکیده
Abstract In this article, we study an initial-boundary value problem for a three-phase field model of nonisothermal solidification processes in the case two possible crystallization states. The governing equations are three phase-field coupled with nonlinear heat equation. Each equation has strong nonlinearities involving higher-order derivatives. We prove existence global-in-time weak solutions to our one-dimensional case.
منابع مشابه
Global Weak Solutions for an Incompressible Charged Fluid with Multi-Scale Couplings: Initial-Boundary Value Problem
The Cauchy problem for the Poisson-Nernst-Planck/Navier-Stokes model was investigated by the first author in [Transport Theory Statist. Phys. 31 (2002), 333–366], where a local existence-uniqueness theory was demonstrated, based upon Kato’s framework for examining evolution equations. In this article, the existence of a global weak solution is proved to hold for the model, in the case of the in...
متن کاملGlobal Weak Solutions for the Initial–Boundary-Value Problems to the Vlasov–Poisson–Fokker–Planck System
This work is devoted to prove the existence of weak solutions of the kinetic Vlasov—Poisson— Fokker—Planck system in bounded domains for attractive or repulsive forces. Absorbing and reflectiontype boundary conditions are considered for the kinetic equation and zero values for the potential on the boundary. The existence of weak solutions is proved for bounded and integrable initial and boundar...
متن کاملPositive solutions for discrete fractional initial value problem
In this paper, the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement .The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz f...
متن کاملExistence of positive solutions for a boundary value problem of a nonlinear fractional differential equation
This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.
متن کاملSolutions to a Three-Point Boundary Value Problem
By using the fixed-point index theory and Leggett-Williams fixed-point theorem,we study the existence of multiple solutions to the three-point boundary value problem u′′′ t a t f t, u t , u′ t 0, 0 < t < 1; u 0 u′ 0 0; u′ 1 − αu′ η λ, where η ∈ 0, 1/2 , α ∈ 1/2η, 1/η are constants, λ ∈ 0,∞ is a parameter, and a, f are given functions. New existence theorems are obtained, which extend and comple...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 2022
ISSN: ['1776-0852', '1402-9251']
DOI: https://doi.org/10.1007/s44198-022-00081-6