Numerical analysis of quasilinear parabolic equations under low regularity assumptions
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DOI: 10.1007/s00211-019-01071-5
Abstract: In this paper, we carry out the numerical analysis of a class of quasilinear parabolic equations, where the diffusion coefficient depends on the solution of the partial differential equation. The goal is to prove error… read more here.
Keywords: numerical analysis; analysis; quasilinear parabolic; parabolic equations ... See more keywords
The Quenching Behavior for a Quasilinear Parabolic Equation with Singular Source and Boundary Flux
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DOI: 10.1007/s10883-018-9415-x
Abstract: In this paper, we consider the quenching behavior for a one-dimensional quasilinear parabolic equation with singular source and boundary flux. We show that the quenching occurs only on the boundary in finite time, and derive… read more here.
Keywords: singular source; parabolic equation; source boundary; quasilinear parabolic ... See more keywords
Quasilinear parabolic equations with a degenerate absorption potential
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DOI: 10.1007/s10958-019-04489-2
Abstract: Quasilinear parabolic equations with a degenerate absorption potential are considered. The estimates of all weak solutions of such equations, including large solutions satisfying the blow-up conditions on the parabolic boundary of a domain, are obtained. read more here.
Keywords: quasilinear parabolic; absorption potential; degenerate absorption; parabolic equations ... See more keywords
Classification of certain qualitative properties of solutions for the quasilinear parabolic equations
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DOI: 10.1007/s11425-016-9077-8
Abstract: In this paper, we mainly consider the initial boundary problem for a quasilinear parabolic equation $${u_t} - div\left( {{{\left| {\nabla u} \right|}^{p - 2}}\nabla u} \right) = - {\left| u \right|^{\beta - 1}}u + \alpha… read more here.
Keywords: properties solutions; quasilinear parabolic; qualitative properties; classification certain ... See more keywords
Gradient weighted estimates at the natural exponent for quasilinear parabolic equations
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DOI: 10.1016/j.aim.2019.03.015
Abstract: In this paper, we obtain weighted norm inequalities for the spatial gradients of weak solutions to quasilinear parabolic equations with weights in the Muckenhoupt class $A_{\frac{q}{p}}(\mathbb{R}^{n+1})$ for $q\geq p$ on non-smooth domains. Here the quasilinear… read more here.
Keywords: gradient weighted; natural exponent; estimates natural; quasilinear parabolic ... See more keywords
On the initial-boundary value problem for some quasilinear parabolic equations of divergence form
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DOI: 10.1016/j.jde.2017.08.056
Abstract: Abstract In this paper we give an existence theorem of global classical solution to the initial boundary value problem for the quasilinear parabolic equations of divergence form u t − div { σ ( |… read more here.
Keywords: initial boundary; quasilinear parabolic; value problem; boundary value ... See more keywords
Global solutions in a quasilinear parabolic–parabolic chemotaxis system with decaying diffusivity and consumption of a chemoattractant
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2018.06.001
Abstract: Abstract In this study, we consider the quasilinear parabolic–parabolic chemotaxis model: { u t = ∇ ⋅ ( D ( u ) ∇ u ) − ∇ ⋅ ( S ( u ) ∇ v… read more here.
Keywords: parabolic parabolic; diffusivity; quasilinear parabolic; parabolic chemotaxis ... See more keywords
Some convergence results of waveform relaxation for a class of second-order quasilinear parabolic equations
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DOI: 10.1080/00207160.2020.1759803
Abstract: Waveform relaxation method at the PDE level can simplify the original differential system by several decoupling approaches, which is very useful for the iterative solution of nonlinear differential equations. In this paper, the convergence of… read more here.
Keywords: relaxation; convergence results; quasilinear parabolic; waveform relaxation ... See more keywords
The exponential behavior and stabilizability of quasilinear parabolic stochastic partial differential equation
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DOI: 10.1142/s0219530521500172
Abstract: In this paper, we study the stability of quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The exponential mean square stability and pathwise exponential stability of the… read more here.
Keywords: exponential behavior; partial differential; quasilinear parabolic; stochastic partial ... See more keywords
A quasilinear parabolic problem with a source term and a nonlocal absorption
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DOI: 10.3934/cpaa.2018092
Abstract: We investigate a quasi-linear parabolicproblem with nonlocal absorption, for which the comparison principle is not always available. Thesufficient conditions are established via energy method to guaranteesolution to blow up or not, and the long time… read more here.
Keywords: absorption; problem source; quasilinear parabolic; nonlocal absorption ... See more keywords