Nonlinear parabolic equation with a dynamical boundary condition of diffusive type

2013 ◽  
Vol 222 ◽  
pp. 372-380 ◽  
Author(s):  
Vladimír Vrábel’ ◽  
Marián Slodička
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Nonlinear Parabolic Equation ◽  
Dynamical Boundary Condition ◽  
Nonlinear Parabolic

scholarly journals Global existence and comparison theorem for a nonlinear parabolic equation

2003 ◽  
Vol 67 (3) ◽  
pp. 481-492
Author(s):  
Mahmoud Hesaaraki ◽  
Abbas Moameni
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Comparison Theorem ◽  
Nonlinear Parabolic Equation ◽  
Homogeneous Boundary Condition ◽  
Existence Of Solution ◽  
Boundedness Of Solutions ◽  
Nonlinear Parabolic ◽  
Image Position ◽  
Suitable Initial Data

In this paper we consider a nonlinear parabolic equation with gradient dependent nonlinearities of the form0 < p, q and a, b ∈ ℝ, with homogeneous boundary condition in a bounded domain Ω ⊆ ℝ,N. In the case 0 < p, q ≤ 1 we prove the existence of solution for suitable initial data. A comparison theorem for the solutions with respect to supersoultions and subsolutions is proved. Using these result, uniqueness and boundedness of solutions is studied.

scholarly journals $L^{\infty }$ decay estimates of solutions of nonlinear parabolic equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hui Wang ◽  
Caisheng Chen
Keyword(s):  
Parabolic Equation ◽  
Weak Solutions ◽  
Nonlinear Parabolic Equation ◽  
Divergence Form ◽  
Decay Estimates ◽  
Laplacian Equation ◽  
Estimates Of Solutions ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear ◽  
Doubly Nonlinear Parabolic Equation

AbstractIn this paper, we are interested in $L^{\infty }$ L ∞ decay estimates of weak solutions for the doubly nonlinear parabolic equation and the degenerate evolution m-Laplacian equation not in the divergence form. By a modified Moser’s technique we obtain $L^{\infty }$ L ∞ decay estimates of weak solutiona.

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