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<p>We consider a parabolic inclusion with an upper semicontinuous multivalued interaction function satisfying the sign and growth conditions of the reaction-diffusion type. We prove the global solvability of the corresponding initial-boundary-value problem in the phase space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> and establish the existence of a global attractor. The conditions for boundedness of the attractor in the space <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation> are obtained.</p>

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GLOBAL SOLVABILITY AND ATTRACTORS FOR A PARABOLIC INCLUSION WITH UPPER SEMICONTINUOUS POLYNOMIAL RIGHT-HAND SIDE

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Oleksiy Kapustyan,
  • Oleksandr Stanzhytskyi,
  • Yuliya Fedorenko,
  • Vasyl Kravets

摘要

We consider a parabolic inclusion with an upper semicontinuous multivalued interaction function satisfying the sign and growth conditions of the reaction-diffusion type. We prove the global solvability of the corresponding initial-boundary-value problem in the phase space \(L^2\) L 2 and establish the existence of a global attractor. The conditions for boundedness of the attractor in the space \(L^{\infty }\) L ∞ are obtained.