LAUSR

Dynamics of Non-autonomous Quasilinear Degenerate Parabolic Equations: the Non-compact Case

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0 Published in 2021 at "Acta Mathematica Vietnamica"

DOI: 10.1007/s40306-021-00424-3

Abstract: We prove the existence of pullback attractors in various spaces for the following non-autonomous quasilinear degenerate parabolic equations involving weighted p -Laplacian operators on ℝ N $\mathbb {R}^{N}$ ∂ u ∂ t − div (… read more here.

Keywords: autonomous quasilinear; non autonomous; parabolic equations; degenerate parabolic ... See more keywords

Second-Order Uniformly Convergent Richardson Extrapolation Method for Singularly Perturbed Degenerate Parabolic PDEs

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0 Published in 2017 at "International Journal of Applied and Computational Mathematics"

DOI: 10.1007/s40819-017-0380-y

Abstract: This article studies the numerical solution of singularly perturbed degenerate parabolic convection–diffusion problem on a rectangular domain. The solution of this problem exhibits a boundary layer in the neighborhood of left boundary of the domain.… read more here.

Keywords: singularly perturbed; direction; richardson extrapolation; perturbed degenerate ... See more keywords

The extinction versus the blow-up: Global and non-global existence of solutions of source types of degenerate parabolic equations with a singular absorption.

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0 Published in 2017 at "Journal of Differential Equations"

DOI: 10.1016/j.jde.2017.07.029

Abstract: Abstract We consider nonnegative solutions of degenerate parabolic equations with a singular absorption term and a source nonlinear term: ∂ t u − ( | u x | p − 2 u x ) x… read more here.

Keywords: existence; equations singular; source; parabolic equations ... See more keywords

Moser–Nash kernel estimates for degenerate parabolic equations

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0 Published in 2017 at "Journal of Functional Analysis"

DOI: 10.1016/j.jfa.2016.12.023

Abstract: Abstract In this paper we deal with the Cauchy problem associated to a class of nonlinear degenerate parabolic equations, whose prototype is the parabolic p -Laplacian ( 2 p ∞ ). In his seminal paper,… read more here.

Keywords: kernel estimates; moser nash; estimates degenerate; parabolic equations ... See more keywords

Solvability to some strongly degenerate parabolic problems

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0 Published in 2019 at "Journal of Mathematical Analysis and Applications"

DOI: 10.1016/j.jmaa.2019.02.056

Abstract: Abstract Nonlinear parabolic equations of “divergence form,” u t = ( φ ( u ) ψ ( u x ) ) x , are considered under the assumption that the “material flux,” φ ( u… read more here.

Keywords: solvability strongly; problem; strongly degenerate; value ... See more keywords

Global weak solutions for a degenerate parabolic system modelling seawater intrusion in confined aquifers

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0 Published in 2018 at "Applicable Analysis"

DOI: 10.1080/00036811.2018.1544622

Abstract: ABSTRACT This article is devoted to prove the existence of a non-negative solution for a degenerate parabolic strongly coupled system which arises from seawater intrusion model in confined aquifers. An approximate linear discretized in time… read more here.

Keywords: system; seawater intrusion; global weak; confined aquifers ... See more keywords

Wong–Zakai approximations and attractors for stochastic degenerate parabolic equations on unbounded domains

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0 Published in 2020 at "Stochastics and Dynamics"

DOI: 10.1142/s0219493721500337

Abstract: The Wong–Zakai approximations given by a stationary process and attractors for stochastic degenerate parabolic equations are considered in this paper. We first establish the existence and uniqueness of tempered pullback attractors for the Wong–Zakai approximations… read more here.

Keywords: stochastic degenerate; zakai approximations; parabolic equations; wong zakai ... See more keywords

On the Weak Characteristic Function Method for a Degenerate Parabolic Equation

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0 Published in 2019 at "Journal of Function Spaces"

DOI: 10.1155/2019/9040284

Abstract: 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. It is well known that the classical Fichera-Oleinik theory… read more here.

Keywords: weak characteristic; parabolic equation; method; degenerate parabolic ... See more keywords

Higher integrability for weak solutions to a degenerate parabolic system with singular coefficients

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0 Published in 2019 at "Boundary Value Problems"

DOI: 10.1186/s13661-019-1285-y

Abstract: AbstractIn this paper, we study the degenerate parabolic system uti+Xα∗(aijαβ(z)Xβuj)=gi(z,u,Xu)+Xα∗fiα(z,u,Xu),$$ u_{t}^{i} + X_{\alpha }^{*} \bigl(a_{ij}^{\alpha \beta }(z){X_{\beta }} {u^{j}}\bigr) = {g_{i}}(z,u,Xu) + X_{\alpha }^{*} f_{i}^{\alpha }(z,u,Xu), $$ where X={X1,…,Xm}$X=\{X_{1},\ldots,X_{m} \}$ is a system of smooth… read more here.

Keywords: parabolic system; system; weak solutions; degenerate parabolic ... See more keywords

The nonnegative weak solution of a degenerate parabolic equation with variable exponent growth order

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0 Published in 2020 at "Boundary Value Problems"

DOI: 10.1186/s13661-020-01364-x

Abstract: A degenerate parabolic equation of the form ( | v | β − 1 v ) t = div ( b ( x , t ) | ∇ v | p ( x , t… read more here.

Keywords: parabolic equation; nonnegative weak; degenerate; vert ... See more keywords

Study of Weak Solutions for a Class of Degenerate Parabolic Variational Inequalities with Variable Exponent

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1 Published in 2022 at "Symmetry"

DOI: 10.3390/sym14061255

Abstract: The authors of this text study weak solutions to the variational inequalities with degenerate parabolic operators and symmetric structure in Sobolev spaces with variable exponent. The existence and uniqueness of the solutions are treated by… read more here.

Keywords: study weak; variational inequalities; weak solutions; variable exponent ... See more keywords