边界受控的非线性扩散方程的整体可解性

Global Solvability of Nonlinear Diffusion Equations with Forcing at the Boundary

LI Jian¹, GAO Wenjie², LIU Linlin³

1. Information Technology College, Jilin Agricultural University, Changchun 130118, China;2. Institute of Mathematics, Jilin University, Changchun 130012, China;3. Department of Applied Mathematica, Changchun Taxation College, Changchun 130017, China

Received:2008-01-09 Revised:1900-01-01 Online:2008-09-26 Published:2008-09-26
Contact: GAO Wenjie

Abstract

Abstract: The present paper studied the global existence of nonnegative solutions of onedimensional Newtonian filtration equation with more general boundary fluxes term, reaction, diffusion and convection. The global existence of solutions for such problems was proved by means of a differential inequality involving the L^r+1norms of solutions and the limit solution method, coming to the conclusion that the nonnegative global solution exists.

Key words: filtration equation, boundary value problem, global solvability, global existence, weak solution

CLC Number:

O175.8

LI Jian, GAO Wenjie, LIU Linlin. Global Solvability of Nonlinear Diffusion Equations with Forcing at the Boundary[J].J4, 2008, 46(05): 801-808.

[1]	TANG Ying, LI Yongxiang. Existence and Uniqueness of Radial Solutions to Elliptic Boundary Value Problem with Gradient Terms on the Unit Ball [J]. Journal of Jilin University Science Edition, 2021, 59(5): 1009-1014.
[2]	WANG Rui, LU Yanqiong. Existence of Positive Solutions for a Class of Semi-positone Second-Order Discrete Periodic Boundary Value Problem with Parameter [J]. Journal of Jilin University Science Edition, 2021, 59(4): 725-730.
[3]	WU Ruofei. Existence and Multiplicity of Positive Solutions for Singular Third-Order Three-Point Boundary Value Problem [J]. Journal of Jilin University Science Edition, 2021, 59(4): 816-820.
[4]	JIANG Weihua, DONG Qian. Existence of Solutions for Three-Point Boundary Value Problems of Conformable Fractional Differential Equations at Resonance [J]. Journal of Jilin University Science Edition, 2021, 59(4): 821-827.
[5]	FU Tongtong, LI Yongxiang. Existence of Positive Radial Solutions for Elliptic Boundary Value Problems with Gradient Terms [J]. Journal of Jilin University Science Edition, 2021, 59(3): 435-443.
[6]	SHANG Shuyan, HAN Xiaoling. Existence of Positive Solutions for Integral Boundary Value Problems of Fractional Differential Equations [J]. Journal of Jilin University Science Edition, 2021, 59(3): 444-450.
[7]	ZHANG Kaibin, CHEN Pengyu. Existence of Positive Solutions for Boundary Value Problems of Fractional Differential Equations in Banach Spaces [J]. Journal of Jilin University Science Edition, 2021, 59(1): 7-12.
[8]	SUN Xiaozhao, LI Yongxiang. Existence of Solutions for a Class of Fully Third-Order Boundary Value Problem [J]. Journal of Jilin University Science Edition, 2021, 59(1): 13-19.
[9]	CHEN Guofang, WU Dan, LV Junliang. A Modified Cel-Centered Finite Volume Method for Solving Filtration Equations [J]. Journal of Jilin University Science Edition, 2020, 58(5): 1135-1141.
[10]	JIA Kaijun. Global Structure of Positive Solution Set for a Class ofSecondOrder Nonlinear Periodic Boundary Value Problems#br# [J]. Journal of Jilin University Science Edition, 2020, 58(4): 761-767.
[11]	FU Tongtong, LI Yongxiang. Existence of Radial Solutions for Elliptic Boundary ValueProblem with Gradient Terms in Exterior Domains [J]. Journal of Jilin University Science Edition, 2020, 58(4): 768-774.
[12]	PENG Zhongqi, LI Yuan, XUE Yimin. Two Positive Solutions of Boundary Value Problem for a Class ofCoupled System of Nonlinear Fractional Differential Equations [J]. Journal of Jilin University Science Edition, 2020, 58(4): 775-781.
[13]	CHEN Huaijun, XU Jianzhong, MO Jiaqi. Shock Layer Solution of Nonlinear Wave System [J]. Journal of Jilin University Science Edition, 2019, 57(3): 493-499.
[14]	WANG Suyun, WEI Jinying, ZHANG Yanhong. Relationship between Number of Zeros of Nonlinear Termand Number of Positive Solutions of Second-OrderPeriodic Boundary Value Problems#br# [J]. Journal of Jilin University Science Edition, 2019, 57(2): 327-330.
[15]	LI Jupeng, LI Yongxiang. Existence of Solution for a Class of Fully n-th OrderOrdinary Differential Boundary Value Problem#br# [J]. Journal of Jilin University Science Edition, 2019, 57(1): 9-14.

Global Solvability of Nonlinear Diffusion Equations with Forcing at the Boundary

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 0