HappyPDEs Conference

Venue

„Simion Stoilow” Mathematical Institute of the Romanian Academy, 21 Calea Griviței, Bucharest,
Miron Nicolescu Amphitheatre, ground floor.

Program and abstracts

Thursday, 11 December 2025

10:00-10:30: Alexandru Pîrvuceanu from Babeș-Bolyai University of Cluj-Napoca will present the talk entitled:
Sharp Hypercontractivity Estimates of the Heat Flow on ${\sf RCD}(0,N)$ Spaces
Abstract:
In this talk, we establish sharp hypercontractivity bounds for the heat flow $({\sf H}_t)_{t\geq 0}$ on ${\sf RCD}(0, N)$ metric measure spaces. The best constant in these estimates involves the asymptotic volume ratio, and its optimality is obtained via the sharp $L^2$-logarithmic Sobolev inequality on ${\sf RCD}(0, N)$ spaces and a blow-down rescaling argument. The equality case in these estimates is completely characterized, and applications of our results include an extension of Li's rigidity result, almost rigidities, as well as topological rigidities of non-collapsed ${\sf RCD}(0, N)$ spaces. This is joint work with Shouhei Honda and Alexandru Kristály.
10:35-11:05: Teodor Rugină from University of Bucharest will present the talk entitled:
Sharp second order inequalities with distance function to the boundary
Abstract:
In this talk, we present generalizations to the $ L^p $−setting, $p>1$, of the Hardy-Rellich inequalities on domains of $\mathbb{R}^N$ with singularity given by the distance function to the boundary. The inequalities we obtain are either sharp or give a new bound for the sharp constant, while also depending on the geometric properties of the domain and its boundary. We also present some applications to the existence and non-existence of non-trivial solutions for a singular problem involving the $p$−Bilaplacian operator. This is a joint work with Cristian Cazacu.
11:10-11:40: Coffee break
11:40-12:10: Fernando Quirós from Universidad Autónoma de Madrid will present the talk entitled:
Traveling wave behavior for Fisher-KPP equations in the hyperbolic space
Abstract:
We study the Cauchy problem in the hyperbolic space for the heat equation with a Fisher-KPP type forcing term. Depending on the relative strength of diffusion, measured by the infimum of the spectrum of the Laplace-Beltrami operator (considered as a positive operator), as compared to the growth due to the forcing term, solutions may propagate or vanish as time goes by. We prove new results concerning this dichotomy that include the critical case where diffusion and reaction are of the same order. When there is propagation, we prove that if the initial datum possesses some symmetry (invariance under a cohomogeneity one subgroup of the group of isometries of the hyperbolic space), the solution converges asymptotically to a (Euclidean) traveling wave of minimal speed in a moving frame. The choice of this frame depends on the subgroup of isometries (elliptic, hyperbolic or parabolic) under which the initial datum is invariant. In contrast with the Euclidean case, the asymptotic spreading speed (in due coordinates) depends on the dimension, while the coefficient of the logarithmic correction does not, no matter the underlying isometry.
Joint work with María del Mar González (U. Autónoma de Madrid & ICMAT) and Irene Gonzálvez (BCAM - Basque Center for Applied Mathematics).
12:10-14:00: Lunch break
14:00-14:30: Andreea Dima from "Simion Stoilow" Mathematical Institute of the Romanian Academy will present the talk entitled:
Galerkin approximation of the fractional Sobolev constant
Abstract:
In this talk we look for sharp accuracy estimates for the optimal constant of the fractional Sobolev inequality in dimension $N\geq 2$, with fractional exponent $s\in (0,1)$. The convergence rates that we establish take place for the Galerkin approximation with piecewise linear elements, when the computations are carried out in the unit ball, for which we employ a quasi-uniform and regular mesh.
14:35-15:05: Dragoș Manea and Radu-Adrian Mihai from "Simion Stoilow" Mathematical Institute of the Romanian Academy and National University of Science and Technology Politehnica Bucharest will present the talk entitled:
Time-based air traffic trajectory model and optimisation
Abstract:
The aim of this project is to optimise flight trajectories for multiple aircraft confined to a specific two-dimensional airspace. The trajectories are generated according to Visual Flight Rules (VFR), meaning that navigation is based on the visual determination of the aircraft's position relative to surrounding landmarks that are well-known both to the controller and pilots. In our model, these points are fixed within the airspace described by a polygonal line. During navigation, aeroplanes are guided towards several points in the airspace, and the air traffic controller is able to instruct the aircraft to head directly to any point at any time.
15:10-15:40: Coffee break
15:40-16:10: Cristian Bereanu from University of Bucharest will present the talk entitled:
Index theory for the Lorentz force equation
Abstract:
In this talk we will explain why the  $S^1$-invariance of the Poincaré action functional associated to the Lorentz force equation gives the existence of multiple critical points which are periodic solutions with a fixed period. Joint work with Alexandru Pirvuceanu.

Friday, 12 December 2025

10:00-10:30: Anisia Teca from University of Craiova will present the talk entitled:
The asymptotic behavior of solutions for a perturbed system of eigenvalue problems
Abstract:
In this talk we present some results about the existence of solutions for a family of perturbed eigenvalue problems described by a system consisting of two partial differential equations in which the differential operators involved are the sum between a $p$-Laplacian and a $q$-Laplacian with $q\neq p$ but depending on $p$. Next, we discuss the asymptotic behavior, as $p\rightarrow\infty$, of the sequence of solutions and we show that, passing eventually to a subsequence, it converges uniformly to a certain limit given by a pair of continuous functions. Moreover, we identify the limiting equations which have as solutions the limiting functions.
10:35-11:05: Andrei Gasparovici from Babeș-Bolyai University of Cluj-Napoca will present the talk entitled:
Natural convection in bidisperse porous media
Abstract:
We study the existence and uniqueness of weak solutions for a steady coupled Boussinesq-type system using a variational approach and fixed-point techniques. This system models the flow of a heat-conducting viscous incompressible fluid in a bidisperse porous medium. Additionally, we present some numerical results regarding natural convection in a differentially heated porous enclosure.
11:10-11:40: Coffee break
11:40-12:10: Ana-Maria Adelina Călina from University of Bucharest will present the talk entitled:
Improved $H^{2}$ Kato regularity for the Laplacian with relatively bounded perturbations
Abstract:
We present regularity results for solutions of elliptic equations with singular coefficients of type $ -\Delta v + \lambda \frac{x\nabla v}{|x|^{2}} = f$ and $ - \Delta v + \lambda \frac{v}{|x|^{2}} = f$. In these cases we refine Kato’s classical regularity result for the Laplacian under relatively bounded perturbations, where Hardy–Rellich-type inequalities play a crucial role. The regularity strongly depends on the value of the spectral parameter $ \lambda$. This talk is based on joint work with Cristian Cazacu. Partially supported by the doctoral fellowship of the University of Bucharest and from the NSF–UEFISCDI grant ROSUA-2024-0001 at IMAR.
12:10-14:00: Lunch break