Results 21 to 30 of about 2,694 (308)

Carleman inequality for a class of super strong degenerate parabolic operators and applications

Electronic Journal of Qualitative Theory of Differential Equations, 2023
In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can not be removed
Bruno Sérgio Araújo, Reginaldo Demarque, Luiz Viana   +2 more
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Stochastic PDEs with multiscale structure [PDF]

, 2012
We study the spatial homogenisation of parabolic linear stochastic PDEs exhibiting a two-scale structure both at the level of the linear operator and at the level of the Gaussian driving noise.
Martin Hairer, Hairer, Martin, Kelly, David (David T. B.), David Kelly   +3 more
core   +1 more source

Fundamental solutions for degenerate parabolic equations [PDF]

Acta Mathematica, 1974
This chapter explains the construction of a candidate for a fundamental solution and the existence, smoothness, and certain bounds for a fundamental solution Γ. The underlying assumptions were that ( a ij , ( x )) is uniformly positive definite and a ij , b i are bounded and uniformly Holder continuous. The chapter presents a proof of how if a ij ,
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Asymptotic expansions for degenerate parabolic equations

Comptes Rendus. Mathématique, 2014
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-time ...
PASCUCCI, ANDREA, Stefano Pagliarani, PAGLIARANI, STEFANO   +2 more
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Discontinuous “viscosity” solutions of a degenerate parabolic equation [PDF]

Transactions of the American Mathematical Society, 1990
We study a nonlinear degenerate parabolic equation of the second order. Regularizing the equation by adding some artificial viscosity, we construct a generalized solution. We show that this solution is not necessarily continuous at all points.
BERTSCH, MICHIEL, Dal Passo R, Ughi, M.
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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

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

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
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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

Admissible conditions for parabolic equations degenerating at infinity [PDF]

St. Petersburg Mathematical Journal, 2008
From the introduction: We investigate existence and uniqueness for bounded solutions of the parabolic Cauchy problem \[ \begin{aligned} \rho\partial_tu= \Delta u\quad &\text{in }\mathbb{R}^n\times \mathbb{R}_+:= S,\\ u= u_0\quad &\text{in }\mathbb{R}^n\times \{0\}\;(n\geq 3).\end{aligned}\tag{1.1} \] Concerning the coefficient \(\rho= \rho(x)\) and the
KAMIN S, POZIO, Maria Assunta, TESEI, Alberto   +2 more
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