 233 Messoud Efendiev, Vitali Vougalter
 Solvability of some Fredholm integrodifferential equations with mixed diffusion in a square
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Jan 30, 23

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Abstract. We demonstrate the existence in the sense of sequences of solutions
for some integrodifferential type problems in a square in two dimensions
with periodic boundary conditions containing the normal diffusion in one
direction and the superdiffusion in the other direction in a constrained
subspace of H^2 using the fixed point technique. The elliptic equation
involves a second order differential operator satisfying the Fredholm
property. It is established that, under the reasonable technical assumptions, the convergence in the appropriate function spaces of the
integral kernels yields the existence and convergence in H_{0}^{2} of
the solutions. We generalize the results obtained in our preceding work
[14] for the analogous equation considered in the whole R^2 which contained a nonFredholm operator.
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