 2236 Messoud Efendiev, Vitali Vougalter
 Solvability of some systems of nonFredholm integrodifferential equations
with mixed diffusion
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Jul 18, 22

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Abstract. We prove the existence in the sense of sequences of solutions for some system of integrodifferential type equations in two dimensions containing the normal diffusion in one direction and the anomalous diffusion in the other direction in H^2(R^2, R^N) using the fixed point technique. The system of elliptic equations contains second order differential operators
without the Fredholm property. It is established that, under the reasonable technical assumptions, the convergence in L^1(R^2) of the integral kernels yields the existence and convergence in H^2(R^2, R^N) of the solutions. We emphasize that the study of the systems is more difficult than of the scalar case and requires to overcome more cumbersome technicalities.
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