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Modified Cauchy Problem with Impulse Action for Parabolic Shilov Equations

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  • Galina Unguryan

Abstract

For parabolic Shilov equations with continuous coefficients, the problem of finding classical solutions that satisfy a modified initial condition with generalized data such as the Gelfand and Shilov distributions is considered. This condition arises in the approximate solution of parabolic problems inverse in time. It linearly combines the meaning of the solution at the initial and some intermediate points in time. The conditions for the correct solvability of this problem are clarified and the formula for its solution is found. Using the results obtained, the corresponding problems with impulse action were solved.

Suggested Citation

  • Galina Unguryan, 2021. "Modified Cauchy Problem with Impulse Action for Parabolic Shilov Equations," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jijmms:v:2021:y:2021:i:1:n:5539676
    DOI: 10.1155/2021/5539676
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    References listed on IDEAS

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    1. Hugo Leiva & Miguel Narvaez & Zoraida Sivoli, 2020. "Controllability of Impulsive Semilinear Stochastic Heat Equation with Delay," International Journal of Differential Equations, Hindawi, vol. 2020, pages 1-10, December.
    2. ., 1995. "Is There a Workers' Movement in Russia?," Chapters, in: The Workers’ Movement in Russia, chapter 7, pages 399-412, Edward Elgar Publishing.
    3. Hugo Leiva, 2015. "Approximate Controllability of Semilinear Impulsive Evolution Equations," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-7, April.
    4. Hugo Leiva, 2015. "Approximate Controllability of Semilinear Impulsive Evolution Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    5. ., 1995. "The Workers'Movement in Russia," Chapters, in: The Workers’ Movement in Russia, chapter 1, pages 1-16, Edward Elgar Publishing.
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