scholarly journals Nonlocal heat equations: Regularizing effect, decay estimates and Nash inequalities

2018 ◽  
Vol 17 (3) ◽  
pp. 1161-1178 ◽  
Author(s):  
Cristina Brändle ◽  
◽  
Arturo De Pablo
Keyword(s):  
Heat Equations ◽  
Decay Estimates ◽  
Nash Inequalities

scholarly journals Global Existence and Decay Estimates of Energy of Solutions for a New Class of p -Laplacian Heat Equations with Logarithmic Nonlinearity

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Salah Mahmoud Boulaaras ◽  
Abdelbaki Choucha ◽  
Abderrahmane Zara ◽  
Mohamed Abdalla ◽  
Bahri-Belkacem Cheri
Keyword(s):  
Global Existence ◽  
Sufficient Conditions ◽  
Research Paper ◽  
Efficient Technique ◽  
Heat Equations ◽  
Decay Estimates ◽  
Source Terms ◽  
Estimates Of Solutions ◽  
New Class ◽  
Analytical Studies

The present research paper is related to the analytical studies of p -Laplacian heat equations with respect to logarithmic nonlinearity in the source terms, where by using an efficient technique and according to some sufficient conditions, we get the global existence and decay estimates of solutions.

Spatial Behavior for Nonlinear Heat Equations

1997 ◽  
Vol 07 (05) ◽  
pp. 633-647 ◽  
Author(s):  
R. Quintanilla
Keyword(s):  
Cross Sections ◽  
Order Approximation ◽  
Three Dimensional ◽  
Spatial Behavior ◽  
Nonlinear Heat Equation ◽  
Heat Equations ◽  
Decay Estimates ◽  
Spatial Estimates ◽  
Comparison Arguments ◽  
First Order Method

In this paper we investigate spatial decay and growth estimates for the solutions of the nonlinear heat equation in a three-dimensional cylinder with homogeneous Dirichlet conditions prescribed on the lateral surface for all time. We derive two Phragmen–Lindelöf type growth–decay estimates. Two methods are used in our approximation. One of them involves a measure on the cross-sections and the other uses the "energy" contained in the part of the cylinder beyond a cross-section. For suitable volumetric heat capacity and thermal conductivitythe second-order approximation combined with comparison arguments allow us to improve the decay estimates. We also sketch the application of the first-order method in the case where the solid is a cone. Spatial estimates for the backward nonlinear equation are presented in the last section.

A Novel Approach for Thermomechanical Analysis of Stationary Rolling Tires within an ALE–Kinematic Framework

2013 ◽  
Vol 41 (3) ◽  
pp. 174-195 ◽  
Author(s):  
Anuwat Suwannachit ◽  
Udo Nackenhorst
Keyword(s):  
Constitutive Model ◽  
Numerical Solutions ◽  
Numerical Technique ◽  
Thermomechanical Analysis ◽  
Rolling Contact ◽  
Computational Technique ◽  
Heat Equations ◽  
Arbitrary Lagrangian Eulerian ◽  
Material Particle ◽  
Operator Split

ABSTRACT A new computational technique for the thermomechanical analysis of tires in stationary rolling contact is suggested. Different from the existing approaches, the proposed method uses the constitutive description of tire rubber components, such as large deformations, viscous hysteresis, dynamic stiffening, internal heating, and temperature dependency. A thermoviscoelastic constitutive model, which incorporates all the mentioned effects and their numerical aspects, is presented. An isentropic operator-split algorithm, which ensures numerical stability, was chosen for solving the coupled mechanical and energy balance equations. For the stationary rolling-contact analysis, the constitutive model presented and the operator-split algorithm are embedded into the Arbitrary Lagrangian Eulerian (ALE)–relative kinematic framework. The flow of material particles and their inelastic history within the spatially fixed mesh is described by using the recently developed numerical technique based on the Time Discontinuous Galerkin (TDG) method. For the efficient numerical solutions, a three-phase, staggered scheme is introduced. First, the nonlinear, mechanical subproblem is solved using inelastic constitutive equations. Next, deformations are transferred to the subsequent thermal phase for the solution of the heat equations concerning the internal dissipation as a source term. In the third step, the history of each material particle, i.e., each internal variable, is transported through the fixed mesh corresponding to the convective velocities. Finally, some numerical tests with an inelastic rubber wheel and a car tire model are presented.

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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