Results 51 to 60 of about 1,099 (88)
The higher integrability of weak solutions of porous medium systems
Advances in Nonlinear Analysis, 2018 In this paper we establish that the gradient of weak solutions to porous medium-type systems admits the self-improving property of higher integrability.
Bögelein Verena +3 more
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On the Two-phase Fractional Stefan Problem
Advanced Nonlinear Studies, 2020 The classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion.
del Teso Félix +2 more
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Advances in Nonlinear AnalysisWe 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,T){Q}_{T}:= \Omega ...
Arora Rakesh, Shmarev Sergey
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A constructive method for convex solutions of a class of nonlinear Black-Scholes equations
Advances in Nonlinear Analysis, 2019 In this work, we are concerned with the theoretical study of a nonlinear Black-Scholes equation resulting from market frictions. We will focus our attention on Barles and Soner’s model where the volatility is enlarged due to the presence of transaction ...
Abounouh Mostafa +3 more
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, 2016 We show how to apply harmonic spaces potential theory in the study of the Dirichlet problem for a general class of evolution hypoelliptic partial differential equations of second order.
Kogoj, Alessia E.
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On some inverse problems for a degenerate parabolic equation with involution
Open MathematicsIn this paper, the solvability of some initial-boundary value problems is considered for a nonlocal analogue of the degenerate parabolic equation. The inverse problems are studied for the case where it is necessary to find not only a solution to the ...
Turmetov Batirkhan, Shalkhar Ainur
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On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with Lévy noise
Advances in Nonlinear Analysis, 2017 In this article, we deal with the stochastic perturbation of degenerate parabolic partial differential equations (PDEs). The particular emphasis is on analyzing the effects of a multiplicative Lévy noise on such problems and on establishing a well ...
Biswas Imran H. +2 more
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Analysis and Geometry in Metric SpacesWe consider degenerate Kolmogorov-Fokker-Planck operators ℒu=∑i,j=1qaij(x,t)uxixj+∑k,j=1Nbjkxkuxj−ut,{\mathcal{ {\mathcal L} }}u=\mathop{\sum }\limits_{i,j=1}^{q}{a}_{ij}\left(x,t){u}_{{x}_{i}{x}_{j}}+\mathop{\sum }\limits_{k,j=1}^{N}{b}_{jk}{x}_{k}{u}_{{
Biagi Stefano, Bramanti Marco
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Near Field Asymptotic Behavior for the Porous Medium Equation on the Half-Line
Advanced Nonlinear Studies, 2017 Kamin and Vázquez [11] proved in 1991 that solutions to the Cauchy–Dirichlet problem for the porous medium equation ut=(um)xx${u_{t}=(u^{m})_{xx}}$, m>1${m>1}$, on the half-line with zero boundary data and nonnegative compactly supported integrable ...
Cortázar Carmen +2 more
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Inverse coefficient problem for Grushin-type parabolic operators
, 2013 The approach to Lipschitz stability for uniformly parabolic equations introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates, seems hard to apply to the case of Grushin-type operators studied in this paper.
Beauchard, Karine, Cannarsa, Piermarco
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