Pub Date : 2023-11-26DOI: 10.1007/s11587-023-00825-6
Giovanni Cimatti
The Galerkin’s method is applied to prove the existence of at least one solution of the initial boundary value problem for the nonlinear system of partial differential equations modelling the electromagnetic heating of materials. In addition a criteria of stability and instability based on a Liapunoff function is presented.
{"title":"Existence of solutions for the problem of microwave heating and a Liapunoff criteria for stability and instability","authors":"Giovanni Cimatti","doi":"10.1007/s11587-023-00825-6","DOIUrl":"https://doi.org/10.1007/s11587-023-00825-6","url":null,"abstract":"<p>The Galerkin’s method is applied to prove the existence of at least one solution of the initial boundary value problem for the nonlinear system of partial differential equations modelling the electromagnetic heating of materials. In addition a criteria of stability and instability based on a Liapunoff function is presented.</p>","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138514766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-04DOI: 10.1007/s11587-023-00822-9
C. Accarino, F. Capone, R. De Luca, G. Massa
Abstract In this paper, a predator–prey model with intraguild predation describing the evolution between three interacting species—namely prey, mesopredator and top predator—is investigated, with the aim to model a complete food web. In particular, the longtime behaviour of the solutions is analysed, proving the existence of an absorbing set, and the linear and nonlinear stability analyses of the coexistence equilibrium are performed.
{"title":"On the dynamics of a Leslie–Gower predator–prey ternary model with intraguild","authors":"C. Accarino, F. Capone, R. De Luca, G. Massa","doi":"10.1007/s11587-023-00822-9","DOIUrl":"https://doi.org/10.1007/s11587-023-00822-9","url":null,"abstract":"Abstract In this paper, a predator–prey model with intraguild predation describing the evolution between three interacting species—namely prey, mesopredator and top predator—is investigated, with the aim to model a complete food web. In particular, the longtime behaviour of the solutions is analysed, proving the existence of an absorbing set, and the linear and nonlinear stability analyses of the coexistence equilibrium are performed.","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135773372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1007/s11587-023-00824-7
Wenbin Yang, Xin Chang
{"title":"Hopf bifurcation and Turing patterns for a diffusive predator–prey system with weak Allee effect","authors":"Wenbin Yang, Xin Chang","doi":"10.1007/s11587-023-00824-7","DOIUrl":"https://doi.org/10.1007/s11587-023-00824-7","url":null,"abstract":"","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135818302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-25DOI: 10.1007/s11587-023-00809-6
Alexander Holguín-Villa, John H. Castillo
Abstract Let $$mathbb {F}G$$ FG denote the group algebra of a locally finite group G over the infinite field $$mathbb {F}$$ F with $$mathop {textrm{char}}nolimits (mathbb {F})ne 2$$ char(F)≠2 , and let $$circledast :mathbb {F}Grightarrow mathbb {F}G$$ ⊛:FG→FG denote the involution defined by $$alpha =Sigma alpha _{g}g mapsto alpha ^circledast =Sigma alpha _{g}sigma (g)g^{*}$$ α=Σαgg↦α⊛=Σαgσ(g)g∗ , where $$sigma :Grightarrow {pm 1}$$ σ:G→{±1} is a group homomorphism (called an orientation) and $$*$$ ∗ is an involution of the group G . In this paper we prove, under some assumptions, that if the $$circledast $$ ⊛ -symmetric units of $$mathbb {F}G$$ FG satisfies a group identity then $$mathbb {F}G$$ FG satisfies a polynomial identity, i.e., we give an affirmative answer to a Conjecture of B. Hartley in this setting. Moreover, in the case when the prime radical $$eta (mathbb {F}G)$$ η(FG)
{"title":"Group identities on symmetric units under oriented involutions in group algebras","authors":"Alexander Holguín-Villa, John H. Castillo","doi":"10.1007/s11587-023-00809-6","DOIUrl":"https://doi.org/10.1007/s11587-023-00809-6","url":null,"abstract":"Abstract Let $$mathbb {F}G$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> denote the group algebra of a locally finite group G over the infinite field $$mathbb {F}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>F</mml:mi> </mml:math> with $$mathop {textrm{char}}nolimits (mathbb {F})ne 2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mtext>char</mml:mtext> <mml:mo>(</mml:mo> <mml:mi>F</mml:mi> <mml:mo>)</mml:mo> <mml:mo>≠</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , and let $$circledast :mathbb {F}Grightarrow mathbb {F}G$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>⊛</mml:mo> <mml:mo>:</mml:mo> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> <mml:mo>→</mml:mo> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> denote the involution defined by $$alpha =Sigma alpha _{g}g mapsto alpha ^circledast =Sigma alpha _{g}sigma (g)g^{*}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mi>Σ</mml:mi> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mi>g</mml:mi> <mml:mo>↦</mml:mo> <mml:msup> <mml:mi>α</mml:mi> <mml:mo>⊛</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:mi>Σ</mml:mi> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mi>σ</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>g</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:msup> <mml:mi>g</mml:mi> <mml:mrow> <mml:mrow /> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , where $$sigma :Grightarrow {pm 1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mo>:</mml:mo> <mml:mi>G</mml:mi> <mml:mo>→</mml:mo> <mml:mo>{</mml:mo> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> is a group homomorphism (called an orientation) and $$*$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mrow /> <mml:mo>∗</mml:mo> </mml:mrow> </mml:math> is an involution of the group G . In this paper we prove, under some assumptions, that if the $$circledast $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>⊛</mml:mo> </mml:math> -symmetric units of $$mathbb {F}G$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> satisfies a group identity then $$mathbb {F}G$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> satisfies a polynomial identity, i.e., we give an affirmative answer to a Conjecture of B. Hartley in this setting. Moreover, in the case when the prime radical $$eta (mathbb {F}G)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>η</mml:mi> <mml:mo>(</mml:mo> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:m","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134972395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-11DOI: 10.1007/s11587-023-00819-4
F. Capone, R. De Luca, L. Fiorentino, V. Luongo, G. Massa
Abstract The aim of this paper is to investigate a reaction-diffusion Leslie–Gower predator–prey model, incorporating the intraguild predation and both self and cross-diffusion. The longtime behaviour of the solutions is analysed, proving the existence of an absorbing set. The existence of patterns is investigated by looking for conditions guaranteeing that an equilibrium, stable in the absence of diffusion, becomes unstable when diffusion is allowed.
{"title":"Turing instability for a Leslie–Gower model","authors":"F. Capone, R. De Luca, L. Fiorentino, V. Luongo, G. Massa","doi":"10.1007/s11587-023-00819-4","DOIUrl":"https://doi.org/10.1007/s11587-023-00819-4","url":null,"abstract":"Abstract The aim of this paper is to investigate a reaction-diffusion Leslie–Gower predator–prey model, incorporating the intraguild predation and both self and cross-diffusion. The longtime behaviour of the solutions is analysed, proving the existence of an absorbing set. The existence of patterns is investigated by looking for conditions guaranteeing that an equilibrium, stable in the absence of diffusion, becomes unstable when diffusion is allowed.","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136209027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-10DOI: 10.1007/s11587-023-00818-5
Marzia Bisi, Maria Groppi, Giorgio Martalò, Cinzia Soresina
{"title":"Correction: A chemotaxis reaction–diffusion model for Multiple Sclerosis with Allee effect","authors":"Marzia Bisi, Maria Groppi, Giorgio Martalò, Cinzia Soresina","doi":"10.1007/s11587-023-00818-5","DOIUrl":"https://doi.org/10.1007/s11587-023-00818-5","url":null,"abstract":"","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136291817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-03DOI: 10.1007/s11587-023-00820-x
Antonio Barletta
Abstract The definitions of temporal instability and of spatial instability in a flow system are comparatively surveyed. The simple model of one-dimensional Burgers’ flow is taken as the scenario where such different conceptions of instability are described. The temporal analysis of instability stems from Lyapunov’s theory, while the spatial analysis of instability interchanges time and space in defining the evolution variable. Thus, the growth rate parameter for temporally unstable perturbations of a basic flow state is to be replaced by a spatial growth rate when a coordinate assumes the role of evolution variable. Finally, the idea of spatial instability is applied to a Rayleigh-Bénard system given by a fluid-saturated horizontal porous layer with an anisotropic permeability and impermeable boundaries kept at different uniform temperatures.
{"title":"Temporal to spatial instability in a flow system: a comparison","authors":"Antonio Barletta","doi":"10.1007/s11587-023-00820-x","DOIUrl":"https://doi.org/10.1007/s11587-023-00820-x","url":null,"abstract":"Abstract The definitions of temporal instability and of spatial instability in a flow system are comparatively surveyed. The simple model of one-dimensional Burgers’ flow is taken as the scenario where such different conceptions of instability are described. The temporal analysis of instability stems from Lyapunov’s theory, while the spatial analysis of instability interchanges time and space in defining the evolution variable. Thus, the growth rate parameter for temporally unstable perturbations of a basic flow state is to be replaced by a spatial growth rate when a coordinate assumes the role of evolution variable. Finally, the idea of spatial instability is applied to a Rayleigh-Bénard system given by a fluid-saturated horizontal porous layer with an anisotropic permeability and impermeable boundaries kept at different uniform temperatures.","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135696078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1007/s11587-023-00821-w
Gaetano Fiore, Monica De Angelis, Renato Fedele, Gabriele Guerriero, Dušan Jovanović
We briefly report and elaborate on some conditions allowing a hydrodynamic description of the impact of a very short and arbitrarily intense laser pulse onto a cold plasma, as well as the localization of the first wave-breaking due to the plasma inhomogeneity. We use a recently developed fully relativistic plane model whereby we reduce the system of the Lorentz-Maxwell and continuity PDEs into a 1-parameter family of decoupled systems of non-autonomous Hamilton equations in dimension 1, with the light-like coordinate $xi=ct!-!z$ replacing time $t$ as an independent variable. Apriori estimates on the Jacobian $hat J$ of the change from Lagrangian to Eulerian coordinates in terms of the input data (initial density and pulse profile) are obtained applying Liapunov direct method to an associated family of pairs of ODEs; wave-breaking is pinpointed by the inequality $hat Jle 0$. These results may help in drastically simplifying the study of extreme acceleration mechanisms of electrons, which have very important applications.
{"title":"Hydrodynamic regime and cold plasmas hit by short laser pulses","authors":"Gaetano Fiore, Monica De Angelis, Renato Fedele, Gabriele Guerriero, Dušan Jovanović","doi":"10.1007/s11587-023-00821-w","DOIUrl":"https://doi.org/10.1007/s11587-023-00821-w","url":null,"abstract":"We briefly report and elaborate on some conditions allowing a hydrodynamic description of the impact of a very short and arbitrarily intense laser pulse onto a cold plasma, as well as the localization of the first wave-breaking due to the plasma inhomogeneity. We use a recently developed fully relativistic plane model whereby we reduce the system of the Lorentz-Maxwell and continuity PDEs into a 1-parameter family of decoupled systems of non-autonomous Hamilton equations in dimension 1, with the light-like coordinate $xi=ct!-!z$ replacing time $t$ as an independent variable. Apriori estimates on the Jacobian $hat J$ of the change from Lagrangian to Eulerian coordinates in terms of the input data (initial density and pulse profile) are obtained applying Liapunov direct method to an associated family of pairs of ODEs; wave-breaking is pinpointed by the inequality $hat Jle 0$. These results may help in drastically simplifying the study of extreme acceleration mechanisms of electrons, which have very important applications.","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135407435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-28DOI: 10.1007/s11587-023-00813-w
Neil Epstein
{"title":"Egyptian integral domains","authors":"Neil Epstein","doi":"10.1007/s11587-023-00813-w","DOIUrl":"https://doi.org/10.1007/s11587-023-00813-w","url":null,"abstract":"","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135386949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-24DOI: 10.1007/s11587-023-00817-6
Hamid Mousavi, Mina Poozesh, Yousef Zamani
{"title":"The impact of the solubilizer of an element on the structure of a finite group","authors":"Hamid Mousavi, Mina Poozesh, Yousef Zamani","doi":"10.1007/s11587-023-00817-6","DOIUrl":"https://doi.org/10.1007/s11587-023-00817-6","url":null,"abstract":"","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135926432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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