Dirichlet conditions at infinity for parabolic and elliptic equations Dedicated to Juan Luis Vázquez, perpetually young and stimulating friend

Shoshana Kamin; Fabio Punzo

doi:10.1016/j.na.2015.11.001

Dirichlet conditions at infinity for parabolic and elliptic equations Dedicated to Juan Luis Vázquez, perpetually young and stimulating friend

Shoshana Kamin
, Fabio Punzo^*

^*Corresponding author for this work

School of Mathematical Sciences

University of Calabria

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in ℝ^N × ℝ₊. Under specific assumptions, we establish existence of solutions satisfying prescribed conditions at infinity, depending on the direction along which infinity is approached. Moreover, the large-time behavior of such solutions is addressed. We consider also elliptic equations in ℝ^N with similar conditions at infinity.

Original language	English
Pages (from-to)	156-175
Number of pages	20
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	138
DOIs	https://doi.org/10.1016/j.na.2015.11.001
State	Published - 1 Jun 2016

Keywords

Conditions at infinity
Parabolic equations
Unbounded coefficients

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10.1016/j.na.2015.11.001

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title = "Dirichlet conditions at infinity for parabolic and elliptic equations Dedicated to Juan Luis V{\'a}zquez, perpetually young and stimulating friend",

abstract = "We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in ℝN {\texttimes} ℝ+. Under specific assumptions, we establish existence of solutions satisfying prescribed conditions at infinity, depending on the direction along which infinity is approached. Moreover, the large-time behavior of such solutions is addressed. We consider also elliptic equations in ℝN with similar conditions at infinity.",

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author = "Shoshana Kamin and Fabio Punzo",

year = "2016",

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doi = "10.1016/j.na.2015.11.001",

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T1 - Dirichlet conditions at infinity for parabolic and elliptic equations Dedicated to Juan Luis Vázquez, perpetually young and stimulating friend

AU - Kamin, Shoshana

AU - Punzo, Fabio

PY - 2016/6/1

Y1 - 2016/6/1

N2 - We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in ℝN × ℝ+. Under specific assumptions, we establish existence of solutions satisfying prescribed conditions at infinity, depending on the direction along which infinity is approached. Moreover, the large-time behavior of such solutions is addressed. We consider also elliptic equations in ℝN with similar conditions at infinity.

AB - We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in ℝN × ℝ+. Under specific assumptions, we establish existence of solutions satisfying prescribed conditions at infinity, depending on the direction along which infinity is approached. Moreover, the large-time behavior of such solutions is addressed. We consider also elliptic equations in ℝN with similar conditions at infinity.

KW - Conditions at infinity

KW - Parabolic equations

KW - Unbounded coefficients

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DO - 10.1016/j.na.2015.11.001

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AN - SCOPUS:84947996470

SN - 0362-546X

VL - 138

SP - 156

EP - 175

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

ER -

Dirichlet conditions at infinity for parabolic and elliptic equations Dedicated to Juan Luis Vázquez, perpetually young and stimulating friend

Abstract

Keywords

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