scholarly journals Relaxation mode of macroscopic plastic deformation in metals

2020 ◽  
pp. 86-88
Author(s):  
Yu.A. Khon ◽  
◽  
L.B. Zuev ◽  
Keyword(s):  
Plastic Deformation ◽  
Parabolic Equation ◽  
Nonlinear Systems ◽  
Unstable Mode ◽  
System Of Nonlinear Equations ◽  
Relaxation Mode ◽  
Deformable Solid ◽  
Spatial And Temporal Scales ◽  
Nonlinear Parabolic ◽  
Macroscopic Plastic Deformation

The relaxation of elastic energy during macroscopic plastic deformation in a strict formulation is determined by the solutions of the system of nonlinear equations of mechanics of a deformable solid. Using the methods of the theory of nonlinear systems, a nonlinear parabolic equation is obtained for the amplitude of an unstable mode, which describes plastic deformation at large spatial and temporal scales.

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.

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.

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