2017
Том 69
№ 9

All Issues

Correct solvability of Solonnikov–Eidel’man parabolic initial-value problems

Ivasyshen S. D., Ivasyuk H. P.

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Abstract

We consider initial-value problems for a new class of systems of equations that combine the structures of Solonnikov parabolic systems and Eidel’man parabolic systems. We prove a theorem on the correct solvability of these problems in Hölder spaces of rapidly increasing functions and obtain an estimate for the norms of solutions via the corresponding norms of the right-hand sides of the problem. For the correctness of this estimate, the condition of the parabolicity of the system is not only sufficient but also necessary.

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 5, pp 775-800.

Citation Example: Ivasyshen S. D., Ivasyuk H. P. Correct solvability of Solonnikov–Eidel’man parabolic initial-value problems // Ukr. Mat. Zh. - 2009. - 61, № 5. - pp. 650-671.

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