Zobrazeno 1 - 10
of 639
pro vyhledávání: '"35C15"'
The excitation of plasmonic nanoparticles by incident electromagnetic waves at frequencies near their subwavelength resonances induces localized heat generation in the surrounding medium. We develop a mathematical framework to rigorously quantify thi
Externí odkaz:
http://arxiv.org/abs/2411.18091
Autor:
Goodwill, Tristan, Epstein, Charles L.
We introduce a new class of computationally tractable scattering problems in unbounded domains, which we call decomposable problems. In these decomposable problems, the computational domain can be split into a finite collection of subdomains in which
Externí odkaz:
http://arxiv.org/abs/2411.11204
Autor:
Rutkowski, Artur
We prove equivalence between nonnegative distributional solutions of the fractional heat equation and caloric functions, i.e., functions satisfying the mean value property with respect to the space-time isotropic $\alpha$-stable process. We also prov
Externí odkaz:
http://arxiv.org/abs/2410.16188
Autor:
Bronsard, Lia, Chen, Jinqi, Mazzouza, Léa, McDonald, Daniel, Singh, Nathan, Stantejsky, Dominik, van Brussel, Lee
We give a brief introduction to a divergence penalized Landau-de Gennes functional as a toy model for the study of nematic liquid crystal with colloid inclusion, in the case of unequal elastic constants. We assume that the nematic occupies the exteri
Externí odkaz:
http://arxiv.org/abs/2410.09930
Autor:
Lastra, Alberto, Malek, Stephane
A novel asymptotic representation of the analytic solutions to a family of singularly perturbed $q-$difference-differential equations in the complex domain is obtained. Such asymptotic relation shows two different levels associated to the vanishing r
Externí odkaz:
http://arxiv.org/abs/2408.12335
Autor:
Botti, Michele, Mascotto, Lorenzo
We prove a Ne\v{c}as-Lions inequality with symmetric gradients on two and three dimensional domains of diameter $R$ that are star-shaped with respect to a ball of radius $\rho$; the constants in the inequality are explicit with respect to $R$ and $\r
Externí odkaz:
http://arxiv.org/abs/2408.00371
Autor:
Shpakivskyi, Vitalii
An infinite-dimensional family of exact solutions of a three-dimensional biharmonic equation was constructed by the hypercomplex method.
Externí odkaz:
http://arxiv.org/abs/2407.09821
Autor:
Ferreira, Raúl, de Pablo, Arturo
We study the blow-up question for the diffusion equation involving a nonlocal derivative in time defined by convolution with a nonnegative and nonincreasing kernel, and a nonlocal operator in space driven by a nonnegative radial L\'evy kernel. We sho
Externí odkaz:
http://arxiv.org/abs/2406.14428
Autor:
Solís, Soveny, Vergara, Vicente
Osgood functions in the source term are used to produce results for non-existence of local solutions into the framework of non-Gaussian diffusion equations. The critical exponent for non-existence of local solutions is found to depend on the fraction
Externí odkaz:
http://arxiv.org/abs/2405.13151
Autor:
Carletti, Lorenzo
We show existence, uniqueness and positivity for the Green's function of the operator $(\Delta_g + \alpha)^k$ in a closed Riemannian manifold $(M,g)$, of dimension $n>2k$, $k\in \mathbb{N}$, $k\geq 1$, with Laplace-Beltrami operator $\Delta_g = -\ope
Externí odkaz:
http://arxiv.org/abs/2403.19341