scholarly journals Existence and uniqueness of bounded weak solutions for some nonlinear parabolic problems

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Weilin Zou ◽  
Juan Li
Keyword(s):  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Parabolic Problems ◽  
Nonlinear Parabolic Problems ◽  
Nonlinear Parabolic ◽  
Bounded Weak Solutions

scholarly journals Nonlinear parabolic problems in unbounded domains

1979 ◽  
Vol 82 (3-4) ◽  
pp. 201-209 ◽  
Author(s):  
Guy Mahler
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Unbounded Domains ◽  
Parabolic Problems ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Nonlinear Parabolic Problems ◽  
Existence Of Weak Solutions ◽  
Nonlinear Parabolic

We show the existence of weak solutions of nonlinear parabolic partial differential equations in unbounded domains, provided that a variant of the Leray-Lions conditions is satisfied.

Renormalised solutions of nonlinear parabolic problems with L1 data: existence and uniqueness

1997 ◽  
Vol 127 (6) ◽  
pp. 1137-1152 ◽  
Author(s):  
D. Blanchard ◽  
F. Murat
Keyword(s):  
Nonlinear Problem ◽  
Existence And Uniqueness ◽  
Dual Space ◽  
Continuous Operator ◽  
Parabolic Problems ◽  
Nonlinear Parabolic Problems ◽  
Test Function ◽  
L1 Data ◽  
Nonlinear Parabolic ◽  
Image Position

In this paper we prove the existence and uniqueness of a renormalised solution of the nonlinear problemwhere the data f and u0 belong to L1(Ω × (0, T)) and L1 (Ω), and where the function a:(0, T) × Ω × ℝN → ℝN is monotone (but not necessarily strictly monotone) and defines a bounded coercive continuous operator from the space into its dual space. The renormalised solution is an element of C0 ([ 0, T] L1 (Ω)) such that its truncates TK(u) belong to withthis solution satisfies the equation formally obtained by using in the equation the test function S(u)φ, where φ belongs to and where S belongs to C∞(ℝ) with

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