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Strömberg, Thomas

Open this publication in new window or tab >>A new proof of indefinite propagation of singularities for a Hamilton-Jacobi equation### Strömberg, Thomas

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2016 (English)In: Journal of evolution equations (Printed ed.), ISSN 1424-3199, E-ISSN 1424-3202, Vol. 16, no 4, p. 895-903Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-6048 (URN)10.1007/s00028-016-0324-8 (DOI)000389353300006 ()2-s2.0-84959375483 (Scopus ID)43dc79c1-711d-46d9-99b8-84a9dcb9e3d9 (Local ID)43dc79c1-711d-46d9-99b8-84a9dcb9e3d9 (Archive number)43dc79c1-711d-46d9-99b8-84a9dcb9e3d9 (OAI)
#####

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##### Note

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

We study propagation of singularities for the Hamilton–Jacobi equation S t +H(∇S)=0,(t,x)∈(0,T)×R n , St+H(∇S)=0,(t,x)∈(0,T)×Rn,where H(p)=12 ⟨p,Ap⟩ H(p)=12⟨p,Ap⟩ is a positive definite quadratic form. Each viscosity solution S S is semiconcave, and it is known that its singularities move along generalized characteristics. We give a new proof of the recent result by Cannarsa et al. (Discrete Contin Dyn Syst 35:4225–4239, 2015), namely that the singularities propagate along generalized characteristics indefinitely forward in time.

Validerad; 2016; Nivå 2; 2016-12-02 (rokbeg)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2019-03-05Bibliographically approvedOpen this publication in new window or tab >>Excess action and broken characteristics for Hamilton-Jacobi equations### Strömberg, Thomas

### Ahmadzadeh, Farzaneh

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2014 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 110, p. 113-129Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-15266 (URN)10.1016/j.na.2014.08.001 (DOI)000342386300009 ()2-s2.0-84906675945 (Scopus ID)ec435aa5-f5c1-45ce-b927-97b51098f949 (Local ID)ec435aa5-f5c1-45ce-b927-97b51098f949 (Archive number)ec435aa5-f5c1-45ce-b927-97b51098f949 (OAI)
#####

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##### Note

Validerad; 2014; 20140801 (strom)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

School of Innovation, Design and Engineering, Mälardalen University.

We study propagation of singularities for Hamilton–Jacobi equations View the MathML sourceSt+H(t,x,∇S)=0,(t,x)∈(0,∞)×Rn,Turn MathJax onby means of the excess Lagrangian action and a related class of characteristics. In a sense, the excess action gauges how far a curve View the MathML sourceX(t) is from being action minimizing for a given viscosity solution S(t,x)S(t,x) of the Hamilton–Jacobi equation. Broken characteristics are defined as curves along which the excess action grows at the slowest pace possible. In particular, we demonstrate that broken characteristics carry the singularities of the viscosity solution.

Open this publication in new window or tab >>Multivariate process parameter change identification by neural network### Ahmadzadeh, Farzaneh

### Lundberg, Jan

### Strömberg, Thomas

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2013 (English)In: The International Journal of Advanced Manufacturing Technology, ISSN 0268-3768, E-ISSN 1433-3015, Vol. 69, no 9-12, p. 2261-2268Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Other Civil Engineering
##### Research subject

Operation and Maintenance
##### Identifiers

urn:nbn:se:ltu:diva-12696 (URN)10.1007/s00170-013-5200-x (DOI)000327095900030 ()2-s2.0-84892371787 (Scopus ID)bdbcaab3-37f3-415c-9607-e6abe6dde418 (Local ID)bdbcaab3-37f3-415c-9607-e6abe6dde418 (Archive number)bdbcaab3-37f3-415c-9607-e6abe6dde418 (OAI)
#####

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##### Note

Validerad; 2013; 20130708 (farahm)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Operation, Maintenance and Acoustics.

Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Operation, Maintenance and Acoustics.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

Whenever there is an out-of-control signal in process parameter control charts, maintenance engineers try to diagnose the cause near the time of the signal which is not always lead to prompt identification of the source(s) of the out-of-control condition and this in some cases yields to extremely high monetary loses for manufacture owner. This paper applies multivariate exponentially weighted moving average (MEWMA) control charts and neural networks to make the signal identification more effective. The simulation of this procedure shows that this new control chart can be very effective in detecting the actual change point for all process dimension and all shift magnitudes considered. This methodology can be used in manufacturing and process industries to predict change points and expedite the search for failure causing parameters, resulting in improved quality at reduced overall cost. This research shows development of MEWMA by usage of neural network for identifying the step change point and the variable responsible for the change in the process mean vector.

Open this publication in new window or tab >>Propagation of singularities along broken characteristics### Strömberg, Thomas

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2013 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 85, p. 93-109Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-12830 (URN)10.1016/j.na.2013.02.024 (DOI)000318378700009 ()2-s2.0-84875493155 (Scopus ID)bfb5b9b0-3da1-4a22-ae95-e2eef9b9bb60 (Local ID)bfb5b9b0-3da1-4a22-ae95-e2eef9b9bb60 (Archive number)bfb5b9b0-3da1-4a22-ae95-e2eef9b9bb60 (OAI)
#####

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##### Note

Validerad; 2013; 20130225 (strom)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

This paper contributes to the analysis of propagation of singularities for semiconcave solutions of Hamilton–Jacobi equations. Under certain conditions, we establish the existence and uniqueness of certain broken characteristics termed strong characteristics. If u is a viscosity solution of a Hamilton–Jacobi equation, then strong characteristics carry the singularities of u.

Open this publication in new window or tab >>A counterexample to uniqueness of generalized characteristics in Hamilton-Jacobi theory### Strömberg, Thomas

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2011 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 7, p. 2758-2762Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-5817 (URN)10.1016/j.na.2010.12.029 (DOI)000288254800028 ()2-s2.0-79951677105 (Scopus ID)400b7377-5b9d-4a0a-ac27-67972888a43a (Local ID)400b7377-5b9d-4a0a-ac27-67972888a43a (Archive number)400b7377-5b9d-4a0a-ac27-67972888a43a (OAI)
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##### Note

Validerad; 2011; 20101229 (strom)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

The notion of generalized characteristics plays a pivotal role in the study of propagation of singularities for Hamilton{Jacobi equations. This note gives an example of nonuniqueness of forward generalized characteristics emanating from a given point.

Open this publication in new window or tab >>A system of the Hamilton-Jacobi and the continuity equations in the vanishing viscosity limit### Strömberg, Thomas

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2011 (English)In: Communications on Pure and Applied Analysis, ISSN 1534-0392, E-ISSN 1553-5258, Vol. 10, no 2, p. 479-506Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-7815 (URN)10.3934/cpaa.2011.10.479 (DOI)000285790600005 ()2-s2.0-82155186063 (Scopus ID)63b77220-8695-11df-8806-000ea68e967b (Local ID)63b77220-8695-11df-8806-000ea68e967b (Archive number)63b77220-8695-11df-8806-000ea68e967b (OAI)
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##### Note

Validerad; 2011; 20100703 (strom)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

We study the following system of the viscous Hamilton-Jacobi and the continuity equations in the limit as epsilon down arrow 0: S-t(epsilon) + 1/2 vertical bar DS epsilon vertical bar(2) + V(x) - epsilon Delta S-epsilon = 0 in Q(T), S-epsilon(0, x) = S-0(x) in R-n; rho(epsilon)(t) + div(rho(epsilon) DS epsilon) = 0 in Q(T), rho(epsilon)(0, x) = rho(0)(x) in R-n. Here Q(T) = (0, T] x R-n. The potential V and the initial function S-0 are allowed to grow quadratically while rho(0) is a Borel measure. The paper justifies and describes the vanishing viscosity transition to the corresponding inviscid system. The notion of weak solution employed for the inviscid system is that of a viscosity-measure solution (S, rho).

Open this publication in new window or tab >>Duality between Frechet differentiability and strong convexity### Strömberg, Thomas

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2011 (English)In: Positivity (Dordrecht), ISSN 1385-1292, E-ISSN 1572-9281, Vol. 15, no 3, p. 527-536Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-15826 (URN)10.1007/s11117-010-0105-5 (DOI)000294503000013 ()2-s2.0-80052277191 (Scopus ID)f62246c0-e8cf-11df-8b36-000ea68e967b (Local ID)f62246c0-e8cf-11df-8b36-000ea68e967b (Archive number)f62246c0-e8cf-11df-8b36-000ea68e967b (OAI)
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##### Note

Validerad; 2011; 20101105 (strom)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

This paper revisits the duality between differentiability and strict or strong convexity under the Legendre-Fenchel transform {Mathematical expression}. Functions f defined on a Banach space X are considered. For a lower semicontinuous but not necessarily convex function f we relate essential Fréchet differentiability of the conjugate function f* to essential strong convexity of f

Open this publication in new window or tab >>On shock generation for Hamilton-Jacobi equations### Strömberg, Thomas

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2011 (English)In: Indagationes mathematicae, ISSN 0019-3577, E-ISSN 1872-6100, Vol. 20, 2009, no 4, p. 619-629Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-15306 (URN)10.1016/S0019-3577(09)80029-3 (DOI)000207877100009 ()2-s2.0-79952431651 (Scopus ID)ecd7c550-b9e4-11df-a707-000ea68e967b (Local ID)ecd7c550-b9e4-11df-a707-000ea68e967b (Archive number)ecd7c550-b9e4-11df-a707-000ea68e967b (OAI)
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##### Note

Validerad; 2011; 20100906 (strom)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

The subject of this paper is the generation of singularities of solutions of Hamilton-Jacobi equations set in (0, ∞) × fordataofclass C∞. Shockwaves originate from conjugate points. To show sharpness of a known Hausdorff estimate, an example is given in which the set of conjugate, regular points includes uncountably many affine subspaces of dimension n − 1.

Open this publication in new window or tab >>On a viscous Hamilton-Jacobi equation with an unbounded potential term### Strömberg, Thomas

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2010 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 73, no 6, p. 1802-1811Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Mathematics, Matematik
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-15714 (URN)10.1016/j.na.2010.05.015 (DOI)000280220200030 ()2-s2.0-77953958394 (Scopus ID)f431b070-a682-11de-8293-000ea68e967b (Local ID)f431b070-a682-11de-8293-000ea68e967b (Archive number)f431b070-a682-11de-8293-000ea68e967b (OAI)
#####

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##### Note

Validerad; 2010; 20090921 (strom)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

We present comparison, uniqueness and existence results for unbounded solutions of a viscous Hamilton-Jacobi or eikonal equation. The equation includes an unbounded potential term V(x) subject to a quadratic upper bound. The results are obtained through a tailor-made change of variables in combination with the Hopf-Cole transformation. An integral representation formula for the solution of the Cauchy problem is derived in the case where V(x)=ω2x2/2

Open this publication in new window or tab >>On the Hamilton-Jacobi equation for a harmonic oscillator### Strömberg, Thomas

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2010 (English)In: Results in Mathematics, ISSN 1422-6383, Vol. 57, no 3-4, p. 195-204Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-7630 (URN)10.1007/s00025-010-0017-5 (DOI)000278096800001 ()2-s2.0-77953023747 (Scopus ID)607652a0-a682-11de-8293-000ea68e967b (Local ID)607652a0-a682-11de-8293-000ea68e967b (Archive number)607652a0-a682-11de-8293-000ea68e967b (OAI)
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_j_idt359",{id:"formSmash:j_idt184:9:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_j_idt359",multiple:true});
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##### Note

Validerad; 2010; 20090921 (strom)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

The topic of this note is the classical Hamilton-Jacobi equation {Mathematical expression}In complete generality, a description of the superdifferential {Mathematical expression} of the viscosity solution of the initial-value problem for this equation is furnished in terms of a convex hull construction and rotations. For background, the basic existence and uniqueness properties of the viscosity solution S are recalled.