一类非局部扩散方程解的局部存在性和唯一性
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摘要
主要研究了一类非局部扩散方程解的局部存在性和唯一性.由于非局部扩散的特殊性,采用Banach不动点定理分别得到了Cauchy问题,Dirichlet和Neumann初边值问题下解的局部存在性和唯一性.
This paper deals with the local existence and uniqueness of solutions for a type of nonlocal diffusion equations. Due to the characteristic of nonlocal diffusion, the local existence and uniqueness of solutions for Cauchy problem,Dirichlet and Neumann initial boundary value problems by Banach fixed point theorem respectively were all obtained.
This paper deals with the local existence and uniqueness of solutions for a type of nonlocal diffusion equations. Due to the characteristic of nonlocal diffusion, the local existence and uniqueness of solutions for Cauchy problem,Dirichlet and Neumann initial boundary value problems by Banach fixed point theorem respectively were all obtained.
引文
[1]BOGOYA M.Blowing up boundary conditions for a nonlocal nonlinear diffusion equation in several space dimensions[J].Nonlinear Analysis Theory Methods Applications,2010,72(1):143-150.
[2]BOGOYA M.A nonlocal nonlinear diffusion equation in higher space dimensions[J].Journal of Mathematical Analysis Applications,2008,344(2):601-615.
[3]CORTAZAR C,ELGUETA M,ROSSI J D.A nonlocal diffusion equation whose solutions develop a free boundary[J].Annales Henri Poincaré,2005,6(2):269-281.
[4]CORTAZAR C,ELGUETA M,ROSSI J D,et al.How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems[J].Archive for Rational Mechanics Analysis,2008,187(1):137-156.
[5]CORTAZAR C,ELGUETA M,ROSSI J D.Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions[J].Israel Journal of Mathematics,2009,170(1):53-60.
[6]张敏华,曾有栋.Dirichlet边界条件下带有反应项的非局部扩散方程组解的全局存在[J].福州大学学报(自然科学版),2015,43(6):727-732.
[7]CHEN Y,ZHU Y.Blow-up results for evolution problems with inhomogeneous nonlocal diffusion[J].Journal of Mathematical Analysis and Applications,2016,444(1):452-463.
[8]BIAN S,CHEN L.A nonlocal reaction diffusion equation and its relation with Fuitta exponent[J].Journal of Mathematical Analysis Applications,2016,444(2):1479-1489.
[9]BIAN S,CHEN L,LATOS E A.Global existence and asymptotic behavior of solutions to a nonlocal Fisher-KPP type problem[J].Nonlinear Analysis,2015,149:165-176.
[10]GARCI A-MELIAN J,QUIROS F.Fujita exponents for evolution problems with nonlocal diffusion[J].Journal of Evolution Equations,2010,10(1):147-161.
[11]COVILLE J.Nonlocal refuge model with a partial control[J].Discrete Continuous Dynamical Systems:Series A,2014,35(4):1421-1446.
[12]SUN J W,LI W T,WANG Z C.A nonlocal dispersal logistic equation with spatial degeneracy[J].Discrete Continuous Dynamical Systems:Series A,2015,35(7):3217-3238.
[13]CHASSEIGEN E,CHAVES M,ROSSI J D.Asymptotic behavior for nonlocal diffusion equations[J].Journal De Mathématiques Pures Et Appliquées,2006,86(3):271-291.
[14]IGNAT L I,ROSSI J D.Refined asymptotic expansions for nonlocal diffusion equations[J].Journal of Evolution Equations,2008,8(4):614-629.
[15]裴海杰,杜宛娟.一类带有反应项的非局部扩散方程在Neumann边界条件的爆破[J].凯里学院学报,2016,34(3):21-25.
[16]BATES P,HAN J.The Neumann boundary problem for a nonlocal Cahn-Hilliard equation[J].Journal of Differential Equations,2015,212(2):235-277.
[2]BOGOYA M.A nonlocal nonlinear diffusion equation in higher space dimensions[J].Journal of Mathematical Analysis Applications,2008,344(2):601-615.
[3]CORTAZAR C,ELGUETA M,ROSSI J D.A nonlocal diffusion equation whose solutions develop a free boundary[J].Annales Henri Poincaré,2005,6(2):269-281.
[4]CORTAZAR C,ELGUETA M,ROSSI J D,et al.How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems[J].Archive for Rational Mechanics Analysis,2008,187(1):137-156.
[5]CORTAZAR C,ELGUETA M,ROSSI J D.Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions[J].Israel Journal of Mathematics,2009,170(1):53-60.
[6]张敏华,曾有栋.Dirichlet边界条件下带有反应项的非局部扩散方程组解的全局存在[J].福州大学学报(自然科学版),2015,43(6):727-732.
[7]CHEN Y,ZHU Y.Blow-up results for evolution problems with inhomogeneous nonlocal diffusion[J].Journal of Mathematical Analysis and Applications,2016,444(1):452-463.
[8]BIAN S,CHEN L.A nonlocal reaction diffusion equation and its relation with Fuitta exponent[J].Journal of Mathematical Analysis Applications,2016,444(2):1479-1489.
[9]BIAN S,CHEN L,LATOS E A.Global existence and asymptotic behavior of solutions to a nonlocal Fisher-KPP type problem[J].Nonlinear Analysis,2015,149:165-176.
[10]GARCI A-MELIAN J,QUIROS F.Fujita exponents for evolution problems with nonlocal diffusion[J].Journal of Evolution Equations,2010,10(1):147-161.
[11]COVILLE J.Nonlocal refuge model with a partial control[J].Discrete Continuous Dynamical Systems:Series A,2014,35(4):1421-1446.
[12]SUN J W,LI W T,WANG Z C.A nonlocal dispersal logistic equation with spatial degeneracy[J].Discrete Continuous Dynamical Systems:Series A,2015,35(7):3217-3238.
[13]CHASSEIGEN E,CHAVES M,ROSSI J D.Asymptotic behavior for nonlocal diffusion equations[J].Journal De Mathématiques Pures Et Appliquées,2006,86(3):271-291.
[14]IGNAT L I,ROSSI J D.Refined asymptotic expansions for nonlocal diffusion equations[J].Journal of Evolution Equations,2008,8(4):614-629.
[15]裴海杰,杜宛娟.一类带有反应项的非局部扩散方程在Neumann边界条件的爆破[J].凯里学院学报,2016,34(3):21-25.
[16]BATES P,HAN J.The Neumann boundary problem for a nonlocal Cahn-Hilliard equation[J].Journal of Differential Equations,2015,212(2):235-277.