Estimates of solutions to some weighted systems defined on ℝ^{ℕ}

2010 ◽  
pp. 89-98
Author(s):  
Jacqueline Fleckinger ◽  
Na Wei
Keyword(s):  
Estimates Of Solutions

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.

scholarly journals Estimates of solutions of elliptic equations with a source reaction term involving the product of the function and its gradient

2019 ◽  
Vol 168 (8) ◽  
pp. 1487-1537 ◽  
Author(s):  
Marie-Françoise Bidaut-Véron ◽  
Marta García-Huidobro ◽  
Laurent Véron
Keyword(s):  
Elliptic Equations ◽  
Reaction Term ◽  
Estimates Of Solutions

scholarly journals NEW L1-GRADIENT TYPE ESTIMATES OF SOLUTIONS TO ONE-DIMENSIONAL QUASILINEAR PARABOLIC SYSTEMS

2010 ◽  
Vol 12 (01) ◽  
pp. 85-106 ◽  
Author(s):  
S. N. ANTONTSEV ◽  
J. I. DÍAZ
Keyword(s):  
Type Equation ◽  
Parabolic Type ◽  
Parabolic Systems ◽  
Diffusion Term ◽  
One Dimensional ◽  
First Order ◽  
Estimates Of Solutions ◽  
Gradient Type ◽  
Degenerate Type ◽  
Parabolic Type Equation

We consider a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of the degenerate type. We derive some new L1-gradient type estimates for its solutions which are uniform in the sense that they do not depend on the coefficients nor on the size of the spatial domain. We also give some applications of such estimates to gas dynamics, filtration problems, a p-Laplacian parabolic type equation and some first order systems of Hamilton–Jacobi or conservation laws type.

scholarly journals Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation

2018 ◽  
Vol 52 (2) ◽  
pp. 567-593 ◽  
Author(s):  
Li Chen ◽  
Simone Göttlich ◽  
Stephan Knapp
Keyword(s):  
Particle System ◽  
Rigorous Derivation ◽  
Uniform Estimates ◽  
Estimates Of Solutions ◽  
Delta Potential ◽  
Intermediate Particle ◽  
Stochastic Particle System ◽  
Aggregation Equation ◽  
Discretization Schemes ◽  
Theoretical Results

In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a stochastic particle system while introducing an intermediate particle system with smooth interaction potential. The theoretical results are compared to numerical simulations relying on suitable discretization schemes for the microscopic and macroscopic level. In particular, the regime switch where the analytic theory fails is numerically analyzed very carefully and allows for a better understanding of the equation.

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