Global Existence for Nonlinear Parabolic Problems With Measure Data– Applications to Non-uniqueness for Parabolic Problems With Critical Gradient terms

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Boumediene Abdellaoui ◽  
Andrea Dall’Aglio ◽  
Ireneo Peral ◽  
Sergio Segura de Léon
Keyword(s):  
Parabolic Equation ◽  
Global Existence ◽  
Present Article ◽  
Open Subset ◽  
Radon Measure ◽  
Nonlinear Parabolic Equation ◽  
Parabolic Problems ◽  
Measure Data ◽  
Nonlinear Parabolic ◽  
Bounded Open Subset

AbstractIn the present article we study global existence for a nonlinear parabolic equation having a reaction term and a Radon measure datum:where 1 < p < N, Ω is a bounded open subset of ℝ

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 $L^{\infty }$ 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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