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• W3020454945 abstract "In this paper, we consider fractional nonclassical diffusion equations under two forms: initial value problem and terminal value problem. For an initial value problem, we study local existence, uniqueness, and continuous dependence of the mild solution. We also present a result on unique continuation and a blow-up alternative for mild solutions of fractional pseudo-parabolic equations. For the terminal value problem, we show the well-posedness of our problem in the case <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=0 greater-than alpha less-than-or-equal-to 1> <mml:semantics> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>></mml:mo> <mml:mi>α<!-- α --></mml:mi> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>0>alpha le 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and show the ill-posedness in the sense of Hadamard in the case <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=alpha greater-than 1> <mml:semantics> <mml:mrow> <mml:mi>α<!-- α --></mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>alpha > 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Then, under the a priori assumption on the exact solution belonging to a Gevrey space, we propose the Fourier truncation method for stabilizing the ill-posed problem. A stability estimate of logarithmic-type in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L Superscript q> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>q</mml:mi> </mml:msup> <mml:annotation encoding=application/x-tex>L^q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> norm is first established." @default.
• W3020454945 created "2020-05-01" @default.
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• W3020454945 date "2020-06-11" @default.
• W3020454945 modified "2023-09-30" @default.
• W3020454945 title "On initial and terminal value problems for fractional nonclassical diffusion equations" @default.
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• W3020454945 doi "https://doi.org/10.1090/proc/15131" @default.
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