arXiv subjects

Kheireddine Biroud

Publications and source records attributed to Kheireddine Biroud.

3 recordsLinked to original sources

arXiv2026

Biharmonic and Interpolating Sesqui-Harmonic Vector Fields with Respect to the varphi-Sasakian Metric

This work investigates biharmonic and interpolating sesqui-harmonic vector fields on the tangent bundle of a para-Kähler--Norden manifold (M, varphi, g) endowed with the varphi-Sasaki metric. We derive the first variation of the bienergy and interpolating sesqui-energy functionals, restricted to the space of vector fields. Explicit characterizations are established for vector fields satisfying the corresponding variational conditions-namely, biharmonicity and interpolating sesqui-harmonicity. Furthermore, several examples are presented to illustrate the general theory and to elucidate the distinctions between harmonic, biharmonic, and interpolating sesqui-harmonic behaviors. These results extend and complement existing research on higher-order harmonicity in pseudo-Riemannian geometry.

math.DG↗

arXiv2025

Global regularity results for the fractional heat equation and application to a class of non-linear KPZ problems

In the first part of this paper, we prove the global regularity, in an adequate parabolic Bessel-Potential space and then in the corresponding parabolic fractional Sobolev space, of the unique solution to following fractional heat equation $ w_t+(-Δ)^sw= h\;;\; w(x,t)=0 \text{ in } \; (\mathbb{R}^N\setminusΩ)\times(0,T)\;;\; w(x,0)=w_0(x) \; \text{in}\; Ω$, where $Ω$ is an open bounded subset of $\mathbb{R}^N$. The proof is based on a new pointwise estimate on the fractional gradient of the corresponding kernel. Moreover, we establish the compactness of $(w_0,h)\mapsto w$. As a majeur application, in the second part , we establish existence and regularity of solutions to a class of Kardar--Parisi--Zhang equations with fractional diffusion and a nonlocal gradient term. Additionally, several auxiliary results of independent interest are obtained.

math.AP↗

arXiv2025

Fractional elliptic reaction-diffusion systems with coupled gradient terms and different diffusion

In this work, we study the existence and nonexistence of nonnegative solutions to a class of nonlocal elliptic systems set in a bounded open subset of $\mathbb{R}^N$. The diffusion operators are of type $u_i\mapsto d_i(-Δ)^{s_i}u_i$ where $0<s_1\neq s_2<1$, and the gradients of the unknowns act as source terms. Existence results are obtained by proving some fine estimates when data belong to weighted Lebesgue spaces. Those estimates are new and interesting in themselves.

math.AP↗