Geodesic
Existence and well-posed results for nonclassical diffusion systems with nonlocal diffusion
Filomat, Tome 37 (2023) no. 24, p. 8289

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DOI

Our goal in this paper is to present well-posed results for nonclassical diffusion systems which have applications in population dynamics. First, we establish the existence and uniqueness of a mild solution to the initial value problem. The asymptotic behavior of the mild solution is also considered when the parameter tends to zero. Second, we obtain a local well-posedness result for nonclassical diffusion systems with a nonlocal time condition. The main idea to obtain the above theoretical results is to use Banach's theorem and some techniques in Fourier series analysis. Some numerical tests are also presented to illustrate the theory.
DOI : 10.2298/FIL2324289T
Classification : 35B65, 35K57, 35K99, 47H10
Keywords: Nonlocal problem, Diffusion system, Existence, Well-posedness 
Nguyen Huy Tuan; Donal O; Regan; Nguyen Huu Can; Mai Quang Vinh. Existence and well-posed results for nonclassical diffusion systems with nonlocal diffusion. Filomat, Tome 37 (2023) no. 24, p. 8289 . doi: 10.2298/FIL2324289T
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     author = {Nguyen Huy Tuan and Donal O and Regan and Nguyen Huu Can and Mai Quang Vinh},
     title = {Existence and well-posed results for nonclassical diffusion systems with nonlocal diffusion},
     journal = {Filomat},
     pages = {8289 },
     year = {2023},
     volume = {37},
     number = {24},
     doi = {10.2298/FIL2324289T},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2324289T/}
}
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