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In this paper, we fully resolve the question of whether the Regularity problem for the parabolic PDE $-\partial_tu + \mbox{div}(A\nabla u)=0$ on a Lipschitz cylinder $\mathcal O\times\mathbb R$ is solvable for some $p\in (1,\infty)$ under the assumpt
Externí odkaz:
http://arxiv.org/abs/2410.23801
Autor:
Arjmand, Doghonay, Marttala, Filip
An accurate approximation of solutions to elliptic problems in infinite domains is challenging from a computational point of view. This is due to the need to replace the infinite domain with a sufficiently large and bounded computational domain, and
Externí odkaz:
http://arxiv.org/abs/2410.15850
We study the optimal control problem of a free boundary PDE model describing the growth of multilayered tumor tissue in vitro. We seek the optimal amount of tumor growth inhibitor that simultaneously minimizes the thickness of the tumor tissue and mi
Externí odkaz:
http://arxiv.org/abs/2410.14114
We carry out a stability and convergence analysis for the fully discrete scheme obtained by combining a finite or virtual element spatial discretization with the upwind-discontinuous Galerkin time-stepping applied to the time-dependent advection-diff
Externí odkaz:
http://arxiv.org/abs/2410.13635
Autor:
Bekmaganbetov, Bekarys, Dong, Hongjie
We investigate the inhomogeneous boundary value problem for elliptic and parabolic equations in divergence form in the half space $\{x_d > 0\}$, where the coefficients are measurable, singular or degenerate, and depend only on $x_d$. The boundary dat
Externí odkaz:
http://arxiv.org/abs/2410.08293
We develop couplings of a recent space-time first-order system least-squares (FOSLS) method for parabolic problems and space-time boundary element methods (BEM) for the heat equation to numerically solve a parabolic transmission problem on the full s
Externí odkaz:
http://arxiv.org/abs/2409.14449
Autor:
Eckardt, Maria, Surulescu, Christina
We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or decay, ac
Externí odkaz:
http://arxiv.org/abs/2409.12657
Autor:
Chorfi, S. E., Maniar, L.
This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to prove null
Externí odkaz:
http://arxiv.org/abs/2409.10302
Autor:
Dindoš, Martin, Sätterqvist, Erika
We study the relationship between the Dirichlet and Regularity problem for parabolic operators of the form $ L = \mbox{div}(A\nabla\cdot) - \partial_t $ on cylindrical domains $ \Omega = \mathcal O \times \mathbb R $, where the base $ \mathcal O \sub
Externí odkaz:
http://arxiv.org/abs/2409.09197
Autor:
Verma, Ram Baran, Mallick, Mohan
This article investigates the exceptional set of the boundary for the following problem: \begin{equation*} \begin{aligned} -\frac{\partial u}{\partial t} + \mathcal{M}_{\lambda,\Lambda}^+(D^2u) + b(x,t)\cdot Du + c(x,t)u =0 \quad \rm{in} ~ \Omega_{T}
Externí odkaz:
http://arxiv.org/abs/2406.03481