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<p>We discuss the time exponential decay of the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p({{\mathbb {R}}}^N)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mi>p</mi> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> norm, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1\le p \le \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>p</mi> <mo>≤</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>, of solutions of a fractional Schrödinger parabolic equation with a locally uniformly integrable potential. The exponential type of the semigroup of solutions is considered and its dependence in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(1\le p \le \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>p</mi> <mo>≤</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation> is addressed. We characterise a large class of potentials for which solutions decay exponentially in time.</p>

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Exponential decay for fractional Schrödinger parabolic problems

  • 期刊论文

  • 发表日期：

    2025年6月16日

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  • Jan W. Cholewa,
  • Anibal Rodriguez-Bernal

摘要

We discuss the time exponential decay of the \(L^p({{\mathbb {R}}}^N)\) L p ( R N ) norm, \(1\le p \le \infty \) 1 ≤ p ≤ ∞ , of solutions of a fractional Schrödinger parabolic equation with a locally uniformly integrable potential. The exponential type of the semigroup of solutions is considered and its dependence in \(1\le p \le \infty \) 1 ≤ p ≤ ∞ is addressed. We characterise a large class of potentials for which solutions decay exponentially in time.