We establish Liouville type theorems in the whole space and in a half-space for parabolic
problems without scale invariance. To this end, we employ two methods, respectively based …

We study necessary conditions and sufficient conditions for the existence of local-in-time
solutions of the Cauchy problem for superlinear fractional parabolic equations. Our …

We show the existence and the uniqueness of initial traces of nonnegative solutions to a
semilinear heat equation on a half space of $\mathbb {R}^ N $ under the zero Dirichlet …

We consider the semilinear heat equation ut-Δ u= f (u) for a large class of non scale invariant
nonlinearities of the form f (u)= up L (u), where p> 1 is Sobolev subcritical and L is a slowly …

Abstract Let 0< θ≤ 2, N≥ 1 and T> 0. We are concerned with the Cauchy problem for the
fractional semilinear parabolic equation∂ tu+(-Δ) θ/2 u= f (u) in RN×(0, T), u (x, 0)= u 0 (x)≥ …

In this paper we obtain necessary conditions and sufficient conditions on the initial data for
the solvability of the Hardy parabolic equation. Using these conditions, we attempt to identify …

We consider the singular nonlinear equation ut− Δ u=|⋅|− γ f (u) in RN×(0, T) with γ> 0 and
f∈ C ([0,∞)) non-decreasing. This equation is known in the literature as the Hardy parabolic …

This paper is devoted to the global in time solvability for a superlinear parabolic equation∂
tu= Δ u+ f (u), x∈ RN, t> 0, u (x, 0)= u 0 (x), x∈ RN,(P) where f (u) denotes superlinear …

This paper focuses on studying the long‐time dynamics of the subordination process for a
range of linear evolution equations, with a special emphasis on the fractional heat equation …

arxiv:2402.14319v1 [math.AP] 22 Feb 2024 Page 1 arxiv:2402.14319v1 [math.AP] 22 Feb 2024
Existence of solutions to a fractional semilinear heat equation in uniformly local weak Zygmund …