Zobrazeno 1 - 10
of 144
pro vyhledávání: '"35k99"'
Autor:
Loher, Amélie
The purpose of this note is to demonstrate the announced result in [Loher, The Strong Harnack inequality for the Boltzmann equation, S\'eminaire Laurent Schwartz proceeding] by filling the gap in the proof sketch. We prove the semi-local Strong Harna
Externí odkaz:
http://arxiv.org/abs/2409.02903
Autor:
Arora, Rakesh, Shmarev, Sergey
We study how the smoothness of the initial datum and the free term affect the global regularity properties of solutions to the Dirichlet problem for the class of parabolic equations of $p(x,t)$-Laplace type %with nonlinear sources depending on the so
Externí odkaz:
http://arxiv.org/abs/2407.20133
Autor:
Loher, Amélie
We derive the Strong Harnack inequality for a class of hypoelliptic integro-differential equations in divergence form. The proof is based on a priori estimates, and as such extends the first non-stochastic approach of the non-local parabolic Strong H
Externí odkaz:
http://arxiv.org/abs/2404.05612
Autor:
Choi, Jae-Hwan
This paper investigates the existence, uniqueness, and regularity of solutions to evolution equations with time-measurable pseudo-differential operators in weighted mixed-norm Sobolev-Lipschitz spaces. We also explore trace embedding and continuity o
Externí odkaz:
http://arxiv.org/abs/2402.03609
Autor:
Arora Rakesh, Shmarev Sergey
Publikováno v:
Advances in Nonlinear Analysis, Vol 13, Iss 1, Pp 25-60 (2024)
We consider the homogeneous Dirichlet problem for the parabolic equation ut−div(∣∇u∣p(x,t)−2∇u)=f(x,t)+F(x,t,u,∇u){u}_{t}-{\rm{div}}({| \nabla u| }^{p\left(x,t)-2}\nabla u)=f\left(x,t)+F\left(x,t,u,\nabla u) in the cylinder QT≔Ω×(0,
Externí odkaz:
https://doaj.org/article/ebbc10516e3747b6887433cdfcbe00e9
Publikováno v:
Demonstratio Mathematica, Vol 57, Iss 1, Pp 295-326 (2024)
In this article, we first study the inverse source problem for parabolic with memory term. We show that our problem is ill-posed in the sense of Hadamard. Then, we construct the convergence result when the parameter tends to zero. We also investigate
Externí odkaz:
https://doaj.org/article/27435d5783684248b0b9f85bed6596e1
In this paper, we develop a physics-informed neural network (PINN) model for parabolic problems with a sharply perturbed initial condition. As an example of a parabolic problem, we consider the advection-dispersion equation (ADE) with a point (Gaussi
Externí odkaz:
http://arxiv.org/abs/2208.08635
Autor:
Loher, Amélie
We derive quantitatively the Harnack inequalities for kinetic integro-differential equations. This implies H\"older continuity. Our method is based on trajectories and exploits a term arising due to the non-locality in the energy estimate. This permi
Externí odkaz:
http://arxiv.org/abs/2203.16137
Autor:
Degtyarev, Sergey
We consider a Cauchy problem for a fractional anisotropic parabolic equation in anisotropic H\"{o}lder spaces. The equation generalizes the heat equation to the case of fractional power of the Laplace operator and the power of this operator can be di
Externí odkaz:
http://arxiv.org/abs/2109.11353
Autor:
Patel, Victoria
We extend the framework of dynamic fracture problems with a phase-field approximation to the case of a nonlinear constitutive relation between the Cauchy stress tensor $ \mathbb{T} $, linearised strain $ \boldsymbol{\epsilon}(\mathbf{u}) $ and strain
Externí odkaz:
http://arxiv.org/abs/2108.03896