Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 78, pp. 1-32.

Title: Solvability of transmission problems with generalized diffusion equation in L^p-spaces

Author: Alexandre Thorel (Normandie Univ., Le Havre, France)
  
Abstract: 
We study a transmission problem in population dynamics between two 
juxtaposed habitats. In each habitat, we consider a generalized
diffusion equation composed by the Laplace operator and a btocould 
be negative or null. Using semigroup theory and functional calculus, 
we give some relation between coefficients to obtain the existence and 
uniqueness of a classical solution in L^p-spaces. 

Submitted April 4, 2024. Published November 30, 2024.
Math Subject Classifications: 5B65, 35J48, 35R20, 47A60, 47D06.
Key Words: Operational differential equations; functional calculus; 
          analytic semigroups; BIP operators; maximal regularity.