Solvability of some integro-differential equations with anomalous diffusion and transport

被引：8
作者：
Vougalter, Vitali [1 ]
Volpert, Vitaly [2 ,3 ,4 ]
机构：
[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada
[2] Univ Lyon 1, Inst Camille Jordan, UMR 5208 CNRS, F-69622 Villeurbanne, France
[3] INRIA Lyon La Doua, INRIA Team Dracula, F-69603 Villeurbanne, France
[4] Peoples Friendship Univ Russia, RUDN Univ, 6 Miklukho Maklaya St, Moscow 117198, Russia
来源：
ANALYSIS AND MATHEMATICAL PHYSICS | 2021年 / 11卷 / 03期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Integro-differential equations; Non Fredholm operators; Sobolev spaces; FREDHOLM; DIRICHLET; SYSTEMS;
D O I：
10.1007/s13324-021-00571-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The article deals with the existence of solutions of an integro-differential equation in the case of anomalous diffusion with the negative Laplace operator in a fractional power in the presence of the transport term. The proof of existence of solutions is based on a fixed point technique. Solvability conditions for elliptic operators without the Fredholm property in unbounded domains are used. We discuss how the introduction of the transport term impacts the regularity of solutions.
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页数：26
相关论文
共 37 条
[1]   Standing lattice solitons in the discrete NLS equation with saturation [J].
Alfimov, G. L. ;
Korobeinikov, A. S. ;
Lustri, C. J. ;
Pelinovsky, D. E. .
NONLINEARITY, 2019, 32 (09) :3445-3484
[2]   Wave Systems with an Infinite Number of Localized Traveling Waves [J].
Alfimov, Georgy L. ;
Medvedeva, Elina V. ;
Pelinovsky, Dmitry E. .
PHYSICAL REVIEW LETTERS, 2014, 112 (05)
[3]   Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator an approach in weighted Sobolev spaces [J].
Amrouche, C ;
Girault, V ;
Giroire, J .
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1997, 76 (01) :55-81
[4]   Mixed exterior Laplace's problem [J].
Amrouche, Cherif ;
Bonzom, Florian .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 338 (01) :124-140
[5]  
BOLLEY P, 1993, J MATH PURE APPL, V72, P105
[6]   Index property in Holderian theory for the Dirichlet exterior problem [J].
Bolley, P ;
Lai, PT .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2001, 26 (1-2) :315-334
[7]   Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence model [J].
Carreras, BA ;
Lynch, VE ;
Zaslavsky, GM .
PHYSICS OF PLASMAS, 2001, 8 (12) :5096-5103
[8]   Spectra of positive and negative energies in the linearized NLS problem [J].
Cuccagna, S ;
Pelinovsky, D ;
Vougalter, V .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2005, 58 (01) :1-29
[9]   Reaction-diffusion systems without the Fredhohn property [J].
Ducrot, A ;
Marion, M ;
Volpert, V .
COMPTES RENDUS MATHEMATIQUE, 2005, 340 (09) :659-664
[10]  
Ducrot A., 2008, ADV DIFF EQU, V13, p1151<plus/minus>1192
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