Partial Differential Equations on Unbounded Domains

2004 ◽  
pp. 58-95
Author(s):  
J. David Logan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Unbounded Domains ◽  
Partial Differential

scholarly journals Nonlinear parabolic problems in unbounded domains

1979 ◽  
Vol 82 (3-4) ◽  
pp. 201-209 ◽  
Author(s):  
Guy Mahler
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Unbounded Domains ◽  
Parabolic Problems ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Nonlinear Parabolic Problems ◽  
Existence Of Weak Solutions ◽  
Nonlinear Parabolic

We show the existence of weak solutions of nonlinear parabolic partial differential equations in unbounded domains, provided that a variant of the Leray-Lions conditions is satisfied.

scholarly journals ON ASYMPTOTIC PROPERTIES OF SOLUTIONS, DEFINED ON THE HALF OF AXIS OF ONE SEMILINEAR ODE

2017 ◽  
Vol 21 (6) ◽  
pp. 130-134
Author(s):  
I.V. Filimonova ◽  
T.S. Khachlaev
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Unknown Function ◽  
Linear Equations ◽  
Unbounded Domains ◽  
Elliptic Partial Differential Equations ◽  
Order Derivative ◽  
Partial Differential ◽  
First Order ◽  
Fowler Equation

The paper deals with the solutions of ordinary differential semi-linear equa- tion, the coefficients of which depend on several real parameters. If the coefficient is chosen so that the equation does not contain the first-order derivative of the unknown function, it will be the case of Emden - Fowler equation. Asymp- totic behavior of Emden - Fowler equation solutions at infinity is described in the book of Richard Bellman. The equations with the first-order derivative, considered in this work, erase in some problems for elliptic partial differential equations in unbounded domains. The sign of the coefficient in first-order deriva- tive term essentially influences on the description of solutions. Partly the result of this paper can be obtained from the works of I.T. Kiguradze. In present work we use lemmas about the behavior of solutions of the linear equations with a strongly (weakly) increasing potential. The paper deals with the solutions of ordinary differential semi-linear equa- tion, the coefficients of which depend on several real parameters. If the coefficient is chosen so that the equation does not contain the first-order derivative of the unknown function, it will be the case of Emden - Fowler equation. Asymp- totic behavior of Emden - Fowler equation solutions at infinity is described in the book of Richard Bellman. The equations with the first-order derivative, considered in this work, erase in some problems for elliptic partial differential equations in unbounded domains. The sign of the coefficient in first-order deriva- tive term essentially influences on the description of solutions. Partly the result of this paper can be obtained from the works of I.T. Kiguradze. In present work we use lemmas about the behavior of solutions of the linear equations with a strongly (weakly) increasing potential.

scholarly journals Sample Paths Properties of Stochastic Processes from Orlicz Spaces, with Applications to Partial Differential Equations

2020 ◽  
Vol 8 (3) ◽  
pp. 722-739
Author(s):  
Lyudmyla Sakhno ◽  
Yuriy Kozachenko ◽  
Enzo Orsingher ◽  
Olha Hopkalo
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Processes ◽  
Orlicz Spaces ◽  
Unbounded Domains ◽  
Partial Differential ◽  
Sample Paths

In the present paper we obtain conditions for stochastic processes from Orlicz spaces to have almost sure bounded and continuous sample paths, the study is concerned with the processes defined on unbounded domains. Estimates for the distributions of suprema of the processes are also presented. Conditions are given in terms of entropy integrals and majorant characteristics of Orlicz spaces. Possible applications to solutions of partial differential equations are discussed. Examples of processes are given for which conditions of the main results are satisfied.

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