DCDS
Strong positivity of continuous supersolutions to parabolic equations with rough boundary data
Dung Le
Discrete & Continuous Dynamical Systems - A 2015, 35(4): 1521-1530 doi: 10.3934/dcds.2015.35.1521
Parabolic equations given on domains with corners are considered. Under very weak assumption on the coefficients, it will be shown that continuous nonnegative supersolutions are strictly positive.
keywords: strong positivity. Parabolic equations
DCDS-B
Global existence and regularity results for strongly coupled nonregular parabolic systems via iterative methods
Dung Le
Discrete & Continuous Dynamical Systems - B 2017, 22(3): 877-893 doi: 10.3934/dcdsb.2017044

The global existence of classical solutions to strongly coupled parabolic systems is shown to be equivalent to the availability of an iterative scheme producing a sequence of solutions with uniform continuity in the BMO norms. Amann's results on global existence of classical solutions still hold under much weaker condition that their BMO norms do not blow up in finite time. The proof makes use of some new global and local weighted Gagliardo-Nirenberg inequalities involving BMO norms.

keywords: Parabolic systems Hölder regularity $A_p$ classes BMO weak solutions
DCDS-B
On the regular set of BMO weak solutions to $p$-Laplacian strongly coupled nonregular elliptic systems
Dung Le
Discrete & Continuous Dynamical Systems - B 2014, 19(10): 3245-3265 doi: 10.3934/dcdsb.2014.19.3245
This paper studies Holder continuity of weak solutions to strongly coupled elliptic systems. We do not assume that the solutions are bounded but BMO and the ellipticity constants can be unbounded.
keywords: BMO weak solutions. Hölder regularity Elliptic systems $A_p$ weights
PROC
Exponential attractors for a chemotaxis growth system on domains of arbitrary dimension
Dung Le
Conference Publications 2003, 2003(Special): 536-543 doi: 10.3934/proc.2003.2003.536
It is proven that there exist exponential attractors for dynamical systems defined by a general chemotaxis system defined on a domain of arbitrary dimension $n$.
keywords: Chemotaxis exponential attractors. reaction diffusion
PROC
Partial regularity of solutions to a class of strongly coupled degenerate parabolic systems
Dung Le
Conference Publications 2005, 2005(Special): 576-586 doi: 10.3934/proc.2005.2005.576
Using the method of heat approximation, we will establish partial regularity results for bounded weak solutions to certain strongly coupled degenerate parabolic systems.
keywords: Parabolic systems Partial Holder regularity. Degenerate systems
DCDS
Higher integrability for gradients of solutions to degenerate parabolic systems
Dung Le
Discrete & Continuous Dynamical Systems - A 2010, 26(2): 597-608 doi: 10.3934/dcds.2010.26.597
Using the method of heat approximation, we will establish higher integrability for the gradients of bounded weak solutions to certain strongly coupled degenerate parabolic systems.
keywords: Parabolic systems Reverse Hölder inequality. Degenerate systems

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