scholarly journals Nonlinear parabolic equation having nonstandard growth condition with respect to the gradient and variable exponent

2021 ◽  
Vol 41 (1) ◽  
pp. 25-53
Author(s):  
Abderrahim Charkaoui ◽  
Houda Fahim ◽  
Nour Eddine Alaa
Keyword(s):  
Fixed Point ◽  
Parabolic Equations ◽  
Variable Exponent ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Quasilinear Parabolic Equations ◽  
Nonstandard Growth ◽  
Nonlinear Parabolic ◽  
Nonstandard Growth Condition ◽  
Quasilinear Parabolic

We are concerned with the existence of solutions to a class of quasilinear parabolic equations having critical growth nonlinearity with respect to the gradient and variable exponent. Using Schaeffer's fixed point theorem combined with the sub- and supersolution method, we prove the existence results of a weak solutions to the considered problems.

scholarly journals Existence of Solutions for a Class of Quasilinear Parabolic Equations with Superlinear Nonlinearities

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zhong-Xiang Wang ◽  
Gao Jia ◽  
Xiao-Juan Zhang
Keyword(s):  
Sobolev Space ◽  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Weighted Sobolev Space ◽  
Boundary Value ◽  
Growth Conditions ◽  
Quasilinear Parabolic Equations ◽  
Superlinear Growth ◽  
Quasilinear Parabolic

Working in a weighted Sobolev space, this paper is devoted to the study of the boundary value problem for the quasilinear parabolic equations with superlinear growth conditions in a domain of RN. Some conditions which guarantee the solvability of the problem are given.

Existence results for some quasilinear parabolic equations

1989 ◽  
Vol 13 (4) ◽  
pp. 373-392 ◽  
Author(s):  
Lucio Boccardo ◽  
FranÇois Murat ◽  
Jean-Pierre Puel
Keyword(s):  
Parabolic Equations ◽  
Existence Results ◽  
Quasilinear Parabolic Equations ◽  
Quasilinear Parabolic

scholarly journals Optimal control of quasilinear parabolic equations

1995 ◽  
Vol 125 (3) ◽  
pp. 545-565 ◽  
Author(s):  
Eduardo Casas ◽  
Luis A. Fernández ◽  
Jiongmin Yong
Keyword(s):  
Optimal Control ◽  
Parabolic Equations ◽  
Optimal Control Problems ◽  
Existence Of Solutions ◽  
State Equation ◽  
Divergence Form ◽  
Control Problems ◽  
Quasilinear Parabolic Equations ◽  
Differentiability Property ◽  
Quasilinear Parabolic

This paper deals with optimal control problems governed by quasilinear parabolic equations in divergence form, whose cost functional is of Lagrangian type. Our aim is to prove the existence of solutions and derive some optimality conditions. To attain this second objective, we accomplish the sensitivity analysis of the state equation with respect to the control, proving that, under some assumptions, this relation is Gâteaux differentiable. Finally, a regularising procedure along with Ekeland's variational principle allow us to treat some other problems for which this differentiability property cannot be stated.

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