Results 31 to 40 of about 1,355,996 (330)

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
doaj   +1 more source

Direct and inverse source problems for degenerate parabolic equations

Journal of Inverse and Ill-Posed Problems, 2020
Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied ...
M.S Hussein, D. Lesnic, V. Kamynin, A. Kostin   +3 more
semanticscholar   +1 more source

The structure of the singular set in the thin obstacle problem for degenerate parabolic equations [PDF]

Calculus of Variations and Partial Differential Equations, 2019
We study the singular set in the thin obstacle problem for degenerate parabolic equations with weight |y|a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage ...
Agnid Banerjee, D. Danielli, N. Garofalo, A. Petrosyan   +3 more
semanticscholar   +1 more source

Nondivergence form degenerate linear parabolic equations on the upper half space [PDF]

Journal of Functional Analysis, 2023
We study a class of nondivergence form second-order degenerate linear parabolic equations in $(-\infty, T) \times {\mathbb R}^d_+$ with the homogeneous Dirichlet boundary condition on $(-\infty, T) \times \partial {\mathbb R}^d_+$, where ${\mathbb R}^d_+
Hongjie Dong, Tuoc V. Phan, H. Tran
semanticscholar   +1 more source

Continuous dependence for BV-entropy solutions to strongly degenerate parabolic equations with variable coefficients [PDF]

, 1999
summary:We consider the Cauchy problem for degenerate parabolic equations with variable coefficients. The equation has nonlinear convective term and degenerate diffusion term which depends on the spatial and time variables.
Carrillo Menéndez, José, Watanabe, Hiroshi   +1 more
core   +1 more source

Well-posedness and stationary solutions [PDF]

, 2011
In this paper we prove existence and uniqueness of variational inequality solutions for a bistable quasilinear parabolic equation arising in the theory of solid-solid phase transitions and discuss its stationary solutions, which can be ...
Grinfeld, Michael, Burns, Martin
core   +4 more sources

An hp-version discontinuous Galerkin method for integro-differential equations of parabolic type [PDF]

, 2011
We study the numerical solution of a class of parabolic integro-differential equations with weakly singular kernels. We use an $hp$-version discontinuous Galerkin (DG) method for the discretization in time.
H. Mustapha, Brunner, Hermann, Schoetzau, D, H. Brunner, D. Schötzau, Mustapha, Kassem, Mustapha, Hussein, K. Mustapha   +7 more
core   +4 more sources

Impulsive Quenching for Degenerate Parabolic Equations

Journal of Mathematical Analysis and Applications, 1996
An impulsive problem for a singular degenerate parabolic equation is studied. Sufficient conditions for the existence of a unique critical length are given. The critical length \(a^*\) is the length of the space interval such that the solution with zero initial and boundary data quenches for intervals larger than \(a^*\) but it exists globally for ...
Chan, C.Y., Kong, P.C.
openaire   +2 more sources

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.
openaire   +4 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