Contents V.12 N.2.2021

  • THE CAUCHY PROBLEM FOR DEGENERATE PARABOLIC CONVOLUTION EQUATION
    HUMMET K. MUSAEV (pp. 278-288)
  • Abstract.

    This paper explores the maximal regularity and separability properties of abstract differential operator equations in weighted spaces. Using Fourier multiplier theorems we will obtain the coercive properties of convolution differential-operator equations (CDOEs) with unbounded operator coefficients in weighted Lp spaces. Finally, these results are applied to establish well-posedness of the Cauchy problem for degenerate parabolic convolution differentialoperator equations. In particular we study the R−positivity of the corresponding convolutionelliptic operators.

    Keywords:

    convolution differential-operator equation, R -positivity, weighted spaces, operatorvalued functions, degenerate convolution equations, weighted multiplier condition, R− boundedness.

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