scholarly journals Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model

2016 ◽  
Vol 13 (6) ◽  
pp. 3-3
Author(s):  
Mohamed M. El-Dessoky ◽  
Ebraheem O. Alzahrani ◽  
Asim M. Asiri ◽  
Meng Fan ◽  
Zijuan Wen ◽  
...  
Keyword(s):  
Parabolic Equation ◽  
Global Existence ◽  
Growth Model ◽  
Existence And Uniqueness ◽  
Quasilinear Parabolic Equation ◽  
Classical Solutions ◽  
Global Existence And Uniqueness ◽  
Quasilinear Parabolic

scholarly journals Global Regularity for the 2D Micropolar Fluid Flows with Mixed Partial Dissipation and Angular Viscosity

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zujin Zhang
Keyword(s):  
Global Existence ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Global Regularity ◽  
Fluid Flows ◽  
Classical Solutions ◽  
Partial Dissipation ◽  
Global Existence And Uniqueness

This paper establishes the global existence and uniqueness of classical solutions to the 2D micropolar fluid flows with mixed partial dissipation and angular viscosity.

scholarly journals Perturbative Cauchy theory for a flux-incompressible Maxwell-Stefan system

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Andrea Bondesan ◽  
Marc Briant
Keyword(s):  
Equilibrium State ◽  
Existence And Uniqueness ◽  
Quasilinear Parabolic Equation ◽  
Strong Solutions ◽  
Cross Diffusion ◽  
Anisotropic Norm ◽  
Exponential Trend ◽  
Perturbative Regime ◽  
Global Existence And Uniqueness ◽  
Quasilinear Parabolic

<p style='text-indent:20px;'>Recently, the authors proved [<xref ref-type="bibr" rid="b2">2</xref>] that the Maxwell-Stefan system with an incompressibility-like condition on the total flux can be rigorously derived from the multi-species Boltzmann equation. Similar cross-diffusion models have been widely investigated, but the particular case of a perturbative incompressible setting around a non constant equilibrium state of the mixture (needed in [<xref ref-type="bibr" rid="b2">2</xref>]) seems absent of the literature. We thus establish a quantitative perturbative Cauchy theory in Sobolev spaces for it. More precisely, by reducing the analysis of the Maxwell-Stefan system to the study of a quasilinear parabolic equation on the sole concentrations and with the use of a suitable anisotropic norm, we prove global existence and uniqueness of strong solutions and their exponential trend to equilibrium in a perturbative regime around any macroscopic equilibrium state of the mixture. As a by-product, we show that the equimolar diffusion condition naturally appears from this perturbative incompressible setting.</p>

REGULARIZATION OF QUASILINEAR HEAT EQUATIONS BY A FRACTIONAL NOISE

2004 ◽  
Vol 04 (02) ◽  
pp. 201-221 ◽  
Author(s):  
DAVID NUALART ◽  
YOUSSEF OUKNINE
Keyword(s):  
Parabolic Equation ◽  
White Noise ◽  
Existence And Uniqueness ◽  
Integrability Condition ◽  
Quasilinear Parabolic Equation ◽  
One Dimension ◽  
Heat Equations ◽  
Fractional Noise ◽  
Uniqueness Of A Solution ◽  
Quasilinear Parabolic

We show the existence and uniqueness of a solution for a quasilinear parabolic equation in one dimension driven by an additive fractional white noise, assuming that the drift is measurable and satisfies a suitable integrability condition. The proof is based on Girsanov theorem and lower estimates of the density of the solution of the equation without drift.

scholarly journals Global existence and uniqueness of the solution to a nonlinear parabolic equation

2018 ◽  
Vol 14 (2) ◽  
pp. 7860-7863
Author(s):  
Alexander G. Ramm
Keyword(s):  
Parabolic Equation ◽  
Global Existence ◽  
Global Solution ◽  
Existence And Uniqueness ◽  
Nonlinear Parabolic Equation ◽  
Unique Global Solution ◽  
Nonlinear Parabolic ◽  
Uniqueness Of The Solution ◽  
Global Existence And Uniqueness

Consider the equation  u’ (t)  -  u + | u |p u = 0, u(0) = u0(x), (1), where u’ := du/dt , p = const > 0, x E R3, t > 0.  Assume that u0 is a smooth and decaying function,           ||u0|| =            sup             |u(x, t)|.                                         x E R3 ,t E R+      It is proved that problem (1) has a unique global solution and this solution satisfies the following estimate                              ||u(x, t)|| < c, where c > 0 does not depend on x, t.

scholarly journals Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Bo Fang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Quasilinear Parabolic Equation ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Blow Up Analysis ◽  
Inner Absorption ◽  
Quasilinear Parabolic

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee thatu(x,t)exists globally or blows up at some finite timet*. Moreover, an upper bound fort*is derived. Under somewhat more restrictive conditions, a lower bound fort*is also obtained.

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