A Cauchy Problem for q-Heat Equation

In this paper, we explore the weak solutions of the Cauchy problem and an inverse source problem for the heat equation in the quantum calculus, formulated in abstract Hilbert spaces. For this, we use the Fourier series expansions. Moreover, we prove the existence, uniqueness, and stability of the weak solution of this problem. For a more detailed analysis and for the proofs of the announced results, we refer to (Ruzhansky M, Shaimardan S, Direct and inverse source problems for heat equation in quantum calculus. https://doi.org/10.48550/arXiv.2212.07403 ).