Absence of Existence and Uniqueness for Forward-backward Parabolic Equations on a Half-line

2010 ◽  
pp. 89-98 ◽  
Author(s):  
P. Binding ◽  
I.M. Karabash
Keyword(s):  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Half Line ◽  
Backward Parabolic Equations

Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities

2016 ◽  
Vol 2016 (712) ◽  
Author(s):  
Michiel Bertsch ◽  
Flavia Smarrazzo ◽  
Alberto Tesei
Keyword(s):  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Quasilinear Parabolic Equation ◽  
Singular Part ◽  
Qualitative Properties ◽  
Power Type ◽  
Radon Measures ◽  
Entropy Inequalities ◽  
Backward Parabolic Equations ◽  
Quasilinear Parabolic

AbstractWe study a quasilinear parabolic equation of forward-backward type, under assumptions on the nonlinearity which hold for a wide class of mathematical models, using a pseudo-parabolic regularization of power type. We prove existence and uniqueness of positive solutions of the regularized problem in a space of Radon measures. It is shown that these solutions satisfy suitable entropy inequalities. We also study their qualitative properties, in particular proving that the singular part of the solution with respect to the Lebesgue measure is constant in time.

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

Conditional stability for backward parabolic equations with LogLipt×Lipx-coefficients

2015 ◽  
Vol 121 ◽  
pp. 101-122 ◽  
Author(s):  
Daniele Del Santo ◽  
Christian P. Jäh ◽  
Martino Prizzi
Keyword(s):  
Parabolic Equations ◽  
Conditional Stability ◽  
Backward Parabolic Equations

scholarly journals Asymptotic Behavior of Solutions of Parabolic Equations with Unbounded Coefficients

1970 ◽  
Vol 37 ◽  
pp. 5-12 ◽  
Author(s):  
Tadashi Kuroda
Keyword(s):  
Asymptotic Behavior ◽  
Euclidean Space ◽  
Parabolic Equations ◽  
Half Line ◽  
Dimensional Euclidean Space ◽  
Asymptotic Behavior Of Solutions ◽  
Unbounded Coefficients ◽  
The Real

Let Rn be the n-dimensional Euclidean space, each point of which is denoted by its coordinate x = (x1,...,xn). The variable t is in the real half line [0, ∞).

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