Pub Date : 2023-12-14DOI: 10.57262/die037-0304-165
Zhuoping Ruan, Ingo Witt
Hyperbolic problems can at times be solved employing symbolic arguments. This is especially true for the construction of forward (and backward) fundamental solutions. We formulate a corresponding abstract scheme and illustrate its practicality by a number of instructive examples.
{"title":"A scheme for solving hyperbolic problems with symbolic structure","authors":"Zhuoping Ruan, Ingo Witt","doi":"10.57262/die037-0304-165","DOIUrl":"https://doi.org/10.57262/die037-0304-165","url":null,"abstract":"Hyperbolic problems can at times be solved employing symbolic arguments. This is especially true for the construction of forward (and backward) fundamental solutions. We formulate a corresponding abstract scheme and illustrate its practicality by a number of instructive examples.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":"25 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139002942","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 : 2023-11-01DOI: 10.57262/die036-1112-1005
Razvan Gabriel Iagar, Philippe Laurençot
The phenomenon of finite time extinction of bounded and non-negative solutions to the diffusion equation with strong absorption $$ partial_t u-Delta u^m+|x|^{sigma}u^q=0, qquad (t,x)in(0,infty)times mathbb R ^N, $$ with $mgeq1$, $qin(0,1)$ and $sigma > 0$, is addressed. Introducing the critical exponent $sigma^* := 2(1-q)/(m-1)$ for $m > 1$ and $sigma^*=infty$ for $m=1$, extinction in finite time is known to take place for $sigmain [0,sigma^*)$ and an alternative proof is provided therein. When $m > 1$ and $sigmage sigma^*$, the occurrence of finite time extinction is proved for a specific class of initial conditions, thereby supplementing results on non-extinction that are available in that range of $sigma$ and showing their sharpness.
{"title":"Finite time extinction for a diffusion equation with spatially inhomogeneous strong absorption","authors":"Razvan Gabriel Iagar, Philippe Laurençot","doi":"10.57262/die036-1112-1005","DOIUrl":"https://doi.org/10.57262/die036-1112-1005","url":null,"abstract":"The phenomenon of finite time extinction of bounded and non-negative solutions to the diffusion equation with strong absorption $$ partial_t u-Delta u^m+|x|^{sigma}u^q=0, qquad (t,x)in(0,infty)times mathbb R ^N, $$ with $mgeq1$, $qin(0,1)$ and $sigma > 0$, is addressed. Introducing the critical exponent $sigma^* := 2(1-q)/(m-1)$ for $m > 1$ and $sigma^*=infty$ for $m=1$, extinction in finite time is known to take place for $sigmain [0,sigma^*)$ and an alternative proof is provided therein. When $m > 1$ and $sigmage sigma^*$, the occurrence of finite time extinction is proved for a specific class of initial conditions, thereby supplementing results on non-extinction that are available in that range of $sigma$ and showing their sharpness.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":"21 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103064","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 : 2023-07-01DOI: 10.57262/die036-0708-621
{"title":"On Coupled Two-Level Variational Problem in Sobolev-Orlicz Space","authors":"","doi":"10.57262/die036-0708-621","DOIUrl":"https://doi.org/10.57262/die036-0708-621","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46468743","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 : 2023-07-01DOI: 10.57262/die036-0708-715
. In this paper we introduce and study a new Kelvin-type transform in the anisotropic setting. In particular, we deal with semilinear and quasilinear anisotropic elliptic problems in the entire space.
{"title":"Anisotropic Kelvin transform","authors":"","doi":"10.57262/die036-0708-715","DOIUrl":"https://doi.org/10.57262/die036-0708-715","url":null,"abstract":". In this paper we introduce and study a new Kelvin-type transform in the anisotropic setting. In particular, we deal with semilinear and quasilinear anisotropic elliptic problems in the entire space.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49027365","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 : 2023-07-01DOI: 10.57262/die036-0708-661
{"title":"On the growth of high Sobolev norms of the fourth-order Schrödinger equation","authors":"","doi":"10.57262/die036-0708-661","DOIUrl":"https://doi.org/10.57262/die036-0708-661","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48353473","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 : 2023-07-01DOI: 10.57262/die036-0708-517
Fang Conghui, Han Zheng
{"title":"The failure of scattering and modified scattering for subcritical Nonlinear Schrödinger equation","authors":"Fang Conghui, Han Zheng","doi":"10.57262/die036-0708-517","DOIUrl":"https://doi.org/10.57262/die036-0708-517","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48608197","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 : 2023-07-01DOI: 10.57262/die036-0708-537
Jifeng Chu, K. Marynets, Zihao Wang
{"title":"Existence and approximate solutions of a nonlinear model for the Antarctic circumpolar current","authors":"Jifeng Chu, K. Marynets, Zihao Wang","doi":"10.57262/die036-0708-537","DOIUrl":"https://doi.org/10.57262/die036-0708-537","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46271081","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 : 2023-07-01DOI: 10.57262/die036-0708-559
Carolina Albarracin, Guillermo Rodriguez-Blanco
{"title":"The IVP for certain generalized dispersion of the zk equation in the cylinder space","authors":"Carolina Albarracin, Guillermo Rodriguez-Blanco","doi":"10.57262/die036-0708-559","DOIUrl":"https://doi.org/10.57262/die036-0708-559","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42949709","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 : 2023-07-01DOI: 10.57262/die036-0708-593
Zhaosheng Feng, Xiaoming He, Yuxi Meng
{"title":"Normalized solutions of fractional Choquard equation with critical nonlinearity","authors":"Zhaosheng Feng, Xiaoming He, Yuxi Meng","doi":"10.57262/die036-0708-593","DOIUrl":"https://doi.org/10.57262/die036-0708-593","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46031118","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 : 2023-07-01DOI: 10.57262/die036-0708-679
{"title":"Existence and stability of traveling waves for $p$-Laplacian equations with time delay","authors":"","doi":"10.57262/die036-0708-679","DOIUrl":"https://doi.org/10.57262/die036-0708-679","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48847463","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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