A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations
Axioms, 2023 We consider a class of nonlinear integro-differential equations that model degenerate nonlocal diffusion. We investigate whether the strong maximum principle is valid for this nonlocal equation. For degenerate parabolic PDEs, the strong maximum principle
Tucker Hartland, Ravi Shankar
doaj +1 more source
Motor‐Free Soft Robots for Cancer Detection, Surgery, and In Situ Bioprinting
Advanced Healthcare Materials, EarlyView.Novel motor‐free soft robots for cancer detection, surgery, and in situ bioprinting–are presented. This master‐slave system is constructed from soft fibrous syringe architectures, removing the need for electrical motors and complex control mechanisms, while reducing the physical tremors.
Chi Cong Nguyen +17 more
wiley +1 more source
On Tricomi Problem of Chaplygin’s Hodograph Equation
Abstract and Applied Analysis, 2015 The existence and uniqueness results for the Tricomi problem of Chaplygin’s hodograph equation are shown, in the case that the domain considered is close to the parabolic degenerate line, by adopting the energy integral methods and choosing judiciously ...
Meng Xu, Li Liu, Hairong Yuan
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On a degenerate parabolic equation from double phase convection
Advances in Difference Equations, 2021 The initial-boundary value problem of a degenerate parabolic equation arising from double phase convection is considered. Let a ( x ) $a(x)$ and b ( x ) $b(x)$ be the diffusion coefficients corresponding to the double phase respectively.
Huashui Zhan
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Emerging Opportunities of Colloidal Quantum Dots for Photocatalytic Organic Transformations
Advanced Materials, EarlyView.Colloidal quantum dots (QDs) have gained significant attention as photocatalysts in organic transformations in recent years. This review highlights QDs’ distinctive features, including the quantum size effect, compositional and structural diversity, tunable surface chemistry, and photophysics.
Qinxuan Cao +4 more
wiley +1 more source
Quasiconformal mappings and degenerate elliptic and parabolic equations
Le Matematiche, 1987 In this paper two Harnak inequalities are proved concerning a degenerate elliptic and a degenerate parabolic equation. In both cases the weight giving the degeneracy is a power of the jacobian of a quasiconformal mapping.
Filippo Chiarenza +1 more
doaj
Singularity and Decay Estimates for a Degenerate Parabolic Equation
Complexity, 2021 In this paper, a degenerate parabolic equation ut−divxθ∇u=xaup with p>1 and ...
Dongyan Li
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Carleman Estimates and Controllability of Stochastic degenerate parabolic Heat Equations [PDF]
arXiv, 2022 This paper concerns the null controllability for a class of stochastic degenerate parabolic equations. We first establish a global Carleman estimate for a linear forward stochastic degenerate equation with multiplicative noise. Using this estimate we prove the null controllability of the backward equation and obtain a partial result for the ...
arxiv
Regularity of a degenerate parabolic equation appearing in Vecer's unified pricing of Asian options
, 2015 Vecer derived a degenerate parabolic equation with a boundary condition characterizing the price of Asian options with generally sampled average. It is well understood that there exists a unique probabilistic solution to such a problem but it remained ...
Dong, Hongjie, Kim, Seick
core +1 more source
Blowup rate of solutions of a degenerate nonlinear parabolic equation
, 2017 We study a nonlinear parabolic equation arising from heat combustion and plane curve evolution problems. Suppose that a solution satisfies a symmetry condition and blows up of type Ⅱ.
Chi-Cheung Poon
semanticscholar +1 more source