Journal
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
Volume 116, Issue 3, Pages -Publisher
SPRINGER-VERLAG ITALIA SRL
DOI: 10.1007/s13398-022-01231-7
Keywords
Nonlocal diffusion; Integrable kernel; Cross-diffusion; Rescaled problem; Convergence; Shigesada-Kawasaki-Teramoto population model
Categories
Funding
- CRUE-CSIC agreement
- Springer Nature
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This study proves that under certain conditions, the nonlocal diffusion problem can be transformed into a problem with local diffusion by rescaling the kernel function. It also provides a new proof of existence for solutions to the local diffusion problem.
We prove that, under a suitable rescaling of the integrable kernel defining the nonlocal diffusion terms, the corresponding sequence of solutions of the Shigesada-Kawasaki-Teramoto nonlocal cross-diffusion problem converges to a solution of the usual problem with local diffusion. In particular, the result may be regarded as a new proof of existence of solutions for the local diffusion problem.
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