Results 21 to 30 of about 307,407 (286)

Expansion of positivity to a class of doubly nonlinear parabolic equations

Electronic Journal of Qualitative Theory of Differential Equations, 2022
We establish the expansion of positivity of the nonnegative, local, weak solutions to the class of doubly nonlinear parabolic equations $$\partial_t (u^{q}) -\operatorname{div}{(|D u|^{p-2} D u)}=0, \qquad\ p>1 \ \text{and} \ q>0$$ considering ...
Eurica Henriques
doaj   +1 more source

Asymptotic expansions for degenerate parabolic equations

Comptes Rendus. Mathématique, 2014
Abstract We prove asymptotic convergence results for some analytical expansions of solutions to degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the uniformly parabolic case, with some a priori bounds on “short cylinders”, and we achieve short ...
PASCUCCI, ANDREA, Stefano Pagliarani, PAGLIARANI, STEFANO   +2 more
openaire   +3 more sources

Embedding Operators in Vector-Valued Weighted Besov Spaces and Applications

Journal of Function Spaces and Applications, 2012
The embedding theorems in weighted Besov-Lions type spaces 𝐵𝑙,𝑠𝑝,𝑞,𝛾 (Ω;𝐸0,𝐸) in which 𝐸0,𝐸 are two Banach spaces and 𝐸0⊂𝐸 are studied. The most regular class of interpolation space 𝐸𝛼 between 𝐸0 and E is found such that the mixed differential operator ...
Veli Shakhmurov
doaj   +1 more source

Degenerate singular parabolic problems with natural growth [PDF]

Opuscula Mathematica
In this paper, we study the existence and regularity results for nonlinear singular parabolic problems with a natural growth gradient term \[\begin{cases}\frac{\partial u}{\partial t}-\operatorname{div}((a(x,t)+u^{q})|\nabla u|^{p-2}\nabla u)+d(x,t)\frac{
Mounim El Ouardy, Youssef El Hadfi, Abdelaaziz Sbai   +2 more
doaj   +1 more source

On the Weak Characteristic Function Method for a Degenerate Parabolic Equation

Journal of Function Spaces, 2019
For a nonlinear degenerate parabolic equation, how to impose a suitable boundary value condition to ensure the well-posedness of weak solutions is a very important problem.
Huashui Zhan
doaj   +1 more source

Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions

Abstract and Applied Analysis, 2006
We consider a class of singularly perturbed parabolic equations for which the degenerate equations obtained by setting the small parameter equal to zero are algebraic equations that have several roots.
Adelaida B. Vasil'eva, Leonid V. Kalachev   +1 more
doaj   +2 more sources

On the viscosity solutions to a degenerate parabolic differential equation [PDF]

Ann. Mat. Pura Appl., Vol 194, Issue 5 (2015), 1423--1454, 2013
In this work, we study some properties of the viscosity solutions to a degenerate parabolic equation involving the non-homogeneous infinity-Laplacian.
arxiv   +1 more source

Optimal Control Problems of a Class of Nonlinear Degenerate Parabolic Equations

Mathematics
The optimal control problems of degenerate parabolic equations have many applications in economics, physics, climatology, and so on. Motivated by the applications, we consider the optimal control problems of a class of nonlinear degenerate parabolic ...
Yang Na, Tianjiao Men, Runmei Du, Yingjie Zhu   +3 more
doaj   +1 more source

Carleman estimates for a stochastic degenerate parabolic equation and applications to null controllability and an inverse random source problem [PDF]

, 2019
In this paper, we establish two Carleman estimates for a stochastic degenerate parabolic equation. The first one is for the backward stochastic degenerate parabolic equation with singular weight function. Combining this Carleman estimate and an approximate argument, we prove the null controllability of the forward stochastic degenerate parabolic ...
arxiv   +1 more source

On the convergence of a class of degenerate parabolic equations

Journal de Mathématiques Pures et Appliquées, 1998
Abstract In this paper we study the convergence of the Cauchy-Dirichlet problems for a sequence of parabolic operators P h = ∂ ∂t − div (a h (x,t) · D) , where the matrices of the coefficient ah(x,t) verify the following degenerate elliptic condition: λ h (x)|ζ| 2 ≤ (a h (x,t)⋯ζ,ζ)≤Lλ h (x)|ζ|
PARONETTO, FABIO, F. Serra Cassano
openaire   +4 more sources