Uniqueness for Cauchy problems for parabolic equations with rapid decay at infinity
Year: 2026
Type: article
Abstract: In this paper, we proved two types of uniqueness results for solutions to parabolic equations whose traces at time T > 0 {T>0} , for large spatial variables satisfy exponential decay assumption. For solutions to parabolic equations in unbounded domains, we can state the main results as follows. The first uniqueness asserts that if | u ( T , x ) | ≤ C e - | x | 2 4 T {|u(T,x)|\leq Ce^{-\frac{|x|^{2}}{4T}}} as | x | → ∞ {|x|\rightarrow\infty} with some T > 0 {T>0} and a potential satisfies some restrictions, then u ( t , x ) = 0 {u(t,x)=0} for 0 < t < T {0 and x ∈ ℝ n {x\in\mathbb{R}^{n}} . The second result asserts that if | u ( t , x ) | + | ∇ u <
Authors: Oleg Imanuvilov, Masahiro Yamamoto
Institutions: Colorado State University, The University of Tokyo
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W7140774455