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math.AP2025
On well-posedness for non-autonomous parabolic Cauchy problems with rough initial data
Hedong Hou
We establish a complete picture for existence, uniqueness, and representation of weak solutions to non-autonomous parabolic Cauchy problems of divergence type. The coefficients are…
math.AP2023
On representation of solutions to the heat equation
Pascal Auscher, Hedong Hou
We propose a simple method to obtain semigroup representation of solutions to the heat equation using a local condition with prescribed growth and a boundedness condition wit…