TY - JOUR

T1 - Well-posedness of the cauchy problem for convection-diffusion equations in uniformly local Lebesgue spaces

AU - Haque, Md Rabiul

AU - Ioku, Norisuke

AU - Ogawa, Takayoshi

AU - Sato, Ryuichi

N1 - Funding Information:
viewers for their careful reading and meaningful suggestions. The second author is partially supported by JSPS Grant-in-aid for Early-Career Scientists (#18K13441) and Fostering Joint International Research A (#19KK0349). The third author is partially supported by JSPS Grant-in-aid for Scientific Research S (#19H05597). The fourth author is partially supported by JSPS Grant-in-aid for Early-Career Scientist (#18K13435).
Publisher Copyright:
© 2021 Differential and Integral Equations.

PY - 2021

Y1 - 2021

N2 - We consider the well-posedness of the Cauchy problem for convection-diffusion equations in uniformly local Lebesgue spaces Lruloc(ℝn). In our setting, an initial function that is spatially periodic or converges to a nonzero constant at infinity is admitted. Our result is applicable to the one dimensional viscous Burgers equation. For the proof, we use the Lpuloc −Lquloc estimate for the heat semigroup obtained by Maekawa-Terasawa [20], the Banach fixed point theorem, and the comparison principle.

AB - We consider the well-posedness of the Cauchy problem for convection-diffusion equations in uniformly local Lebesgue spaces Lruloc(ℝn). In our setting, an initial function that is spatially periodic or converges to a nonzero constant at infinity is admitted. Our result is applicable to the one dimensional viscous Burgers equation. For the proof, we use the Lpuloc −Lquloc estimate for the heat semigroup obtained by Maekawa-Terasawa [20], the Banach fixed point theorem, and the comparison principle.

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M3 - Article

AN - SCOPUS:85107772439

VL - 34

SP - 223

EP - 244

JO - Differential and Integral Equations

JF - Differential and Integral Equations

SN - 0893-4983

IS - 3-4

ER -