Second order unbounded parabolic equations in separated form

Maciej Kocan; Andrzej Święch

Studia Mathematica (1995)

  • Volume: 115, Issue: 3, page 291-310
  • ISSN: 0039-3223

Abstract

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We prove existence and uniqueness of viscosity solutions of Cauchy problems for fully nonlinear unbounded second order Hamilton-Jacobi-Bellman-Isaacs equations defined on the product of two infinite-dimensional Hilbert spaces H'× H'', where H'' is separable. The equations have a special "separated" form in the sense that the terms involving second derivatives are everywhere defined, continuous and depend only on derivatives with respect to x'' ∈ H'', while the unbounded terms are of first order and depend only on derivatives with respect to x' ∈ H'.

How to cite

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Kocan, Maciej, and Święch, Andrzej. "Second order unbounded parabolic equations in separated form." Studia Mathematica 115.3 (1995): 291-310. <http://eudml.org/doc/216214>.

@article{Kocan1995,
abstract = {We prove existence and uniqueness of viscosity solutions of Cauchy problems for fully nonlinear unbounded second order Hamilton-Jacobi-Bellman-Isaacs equations defined on the product of two infinite-dimensional Hilbert spaces H'× H'', where H'' is separable. The equations have a special "separated" form in the sense that the terms involving second derivatives are everywhere defined, continuous and depend only on derivatives with respect to x'' ∈ H'', while the unbounded terms are of first order and depend only on derivatives with respect to x' ∈ H'.},
author = {Kocan, Maciej, Święch, Andrzej},
journal = {Studia Mathematica},
keywords = {second order unbounded parabolic equations; viscosity solutions; Cauchy problems; Hamilton-Jacobi-Bellman-Isaacs equations; infinite-dimensional Hilbert spaces},
language = {eng},
number = {3},
pages = {291-310},
title = {Second order unbounded parabolic equations in separated form},
url = {http://eudml.org/doc/216214},
volume = {115},
year = {1995},
}

TY - JOUR
AU - Kocan, Maciej
AU - Święch, Andrzej
TI - Second order unbounded parabolic equations in separated form
JO - Studia Mathematica
PY - 1995
VL - 115
IS - 3
SP - 291
EP - 310
AB - We prove existence and uniqueness of viscosity solutions of Cauchy problems for fully nonlinear unbounded second order Hamilton-Jacobi-Bellman-Isaacs equations defined on the product of two infinite-dimensional Hilbert spaces H'× H'', where H'' is separable. The equations have a special "separated" form in the sense that the terms involving second derivatives are everywhere defined, continuous and depend only on derivatives with respect to x'' ∈ H'', while the unbounded terms are of first order and depend only on derivatives with respect to x' ∈ H'.
LA - eng
KW - second order unbounded parabolic equations; viscosity solutions; Cauchy problems; Hamilton-Jacobi-Bellman-Isaacs equations; infinite-dimensional Hilbert spaces
UR - http://eudml.org/doc/216214
ER -

References

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