scholarly journals Weak Solutions for Nonlinear Parabolic Equations with Variable Exponents

2017 ◽  
Vol 25 (1) ◽  
pp. 55-70 ◽  
Author(s):  
Lingeshwaran Shangerganesh ◽  
Arumugam Gurusamy ◽  
Krishnan Balachandran
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Degenerate Parabolic Equation ◽  
Nonlinear Parabolic Equations ◽  
Variable Exponents ◽  
Nonlinear Parabolic ◽  
Order Degenerate ◽  
Degenerate Parabolic

Abstract In this work, we study the existence and uniqueness of weak solu- tions of fourth-order degenerate parabolic equation with variable exponent using the di erence and variation methods.

Intrinsic scaling method for doubly nonlinear parabolic equations and its application

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Masashi Misawa ◽  
Kenta Nakamura
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Large Data ◽  
Nonlinear Parabolic Equations ◽  
Sobolev Type ◽  
Scaling Method ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear ◽  
Doubly Nonlinear Equation ◽  
Doubly Nonlinear Parabolic Equation

Abstract In this article, we consider a fast diffusive type doubly nonlinear parabolic equation, called 𝑝-Sobolev type flows, and devise a new intrinsic scaling method to transform the prototype doubly nonlinear equation to the 𝑝-Sobolev type flows. As an application, we show the global existence and regularity for the 𝑝-Sobolev type flows with large data.

Complete blow-up for quasilinear degenerate parabolic equations

2000 ◽  
Vol 130 (4) ◽  
pp. 877-908 ◽  
Author(s):  
R. Suzuki
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equation ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Image Position

Non-negative post-blow-up solutions of the quasilinear degenerate parabolic equation in RN (or a bounded domain with Dirichlet boundary condition) are studied. Various sufficient conditions for complete blow-up of solutions are given.

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