Boundary Value Problems最新文献

{"title":"Spontaneous Resolution of Diplopia Related to a Frontal Sinus Mucocele.","authors":"Jim S Xie, Jonathan A Micieli","doi":"10.1097/WNO.0000000000001530","DOIUrl":"10.1097/WNO.0000000000001530","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"2012 1","pages":"e256-e257"},"PeriodicalIF":2.9,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88055124","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}

{"title":"On the global existence and analyticity of the mild solution for the fractional Porous medium equation","authors":"Muhammad Zainul Abidin, Muhammad Marwan","doi":"10.1186/s13661-023-01794-3","DOIUrl":"https://doi.org/10.1186/s13661-023-01794-3","url":null,"abstract":"Abstract In this research article we focus on the study of existence of global solution for a three-dimensional fractional Porous medium equation. The main objectives of studying the fractional porous medium equation in the corresponding critical function spaces are to show the existence of unique global mild solution under the condition of small initial data. Applying Fourier transform methods gives an equivalent integral equation of the model equation. The linear and nonlinear terms are then estimated in the corresponding Lei and Lin spaces. Further, the analyticity of solution to the fractional Porous medium equation is also obtained.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"42 02","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134900658","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}

{"title":"Riemann problem for a $2times 2$ hyperbolic system with time-gradually-degenerate damping","authors":"Shiwei Li","doi":"10.1186/s13661-023-01798-z","DOIUrl":"https://doi.org/10.1186/s13661-023-01798-z","url":null,"abstract":"Abstract This paper is focused on the Riemann problem for a $2times 2$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:mn>2</mml:mn> </mml:math> hyperbolic system of conservation laws with a time-gradually-degenerate damping. Two kinds of non-self-similar solutions involving the delta-shocks and vacuum are obtained using the variable substitution method. The generalized Rankine-Hugoniot relation and entropy condition are clarified for the delta-shock. Furthermore, the vanishing viscosity method proves the existence, uniqueness, and stability of non-self-similar solutions.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"62 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134901043","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}

{"title":"Enhanced shifted Jacobi operational matrices of derivatives: spectral algorithm for solving multiterm variable-order fractional differential equations","authors":"H. M. Ahmed","doi":"10.1186/s13661-023-01796-1","DOIUrl":"https://doi.org/10.1186/s13661-023-01796-1","url":null,"abstract":"Abstract This paper presents a new way to solve numerically multiterm variable-order fractional differential equations (MTVOFDEs) with initial conditions by using a class of modified shifted Jacobi polynomials (MSJPs). As their defining feature, MSJPs satisfy the given initial conditions. A key aspect of our methodology involves the construction of operational matrices (OMs) for ordinary derivatives (ODs) and variable-order fractional derivatives (VOFDs) of MSJPs and the application of the spectral collocation method (SCM). These constructions enable efficient and accurate numerical computation. We establish the error analysis and the convergence of the proposed algorithm, providing theoretical guarantees for its effectiveness. To demonstrate the applicability and accuracy of our method, we present five numerical examples. Through these examples, we compare the results obtained with other published results, confirming the superiority of our method in terms of accuracy and efficiency. The suggested algorithm yields very accurate agreement between the approximate and exact solutions, which are shown in tables and graphs.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"62 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134900899","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}

{"title":"Decay of the 3D Lüst model","authors":"Ying Sheng","doi":"10.1186/s13661-023-01797-0","DOIUrl":"https://doi.org/10.1186/s13661-023-01797-0","url":null,"abstract":"Abstract In this paper, we consider the time-decay rate of the strong solution to the Cauchy problem for the three-dimensional Lüst model. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. The $dot{H}^{-s}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mover> <mml:mi>H</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:msup> </mml:math> ( $0leq s<frac{3}{2}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mn>0</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>s</mml:mi> <mml:mo><</mml:mo> <mml:mfrac> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> ) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"115 17","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135138378","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}

{"title":"Dynamical behavior of perturbed Gerdjikov–Ivanov equation through different techniques","authors":"Hamood Ur Rehman, Ifrah Iqbal, M. Mirzazadeh, Salma Haque, Nabil Mlaiki, Wasfi Shatanawi","doi":"10.1186/s13661-023-01792-5","DOIUrl":"https://doi.org/10.1186/s13661-023-01792-5","url":null,"abstract":"Abstract The objective of this work is to investigate the perturbed Gerdjikov–Ivanov (GI) equation along spatio-temporal dispersion which explains the dynamics of soliton dispersion and evolution of propagation distance in optical fibers, photonic crystal fibers (PCF), and metamaterials. The algorithms, namely hyperbolic extended function method and generalized Kudryashov’s method, are constructed to obtain the new soliton solutions. The dark, bright, periodic, and singular solitons are derived of the considered equation with the appropriate choice of parameters. These results are novel, confirm the stability of optical solitons, and have not been studied earlier. The explanation of evaluated results is given by sketching the various graphs in 3D, contour and 2D plots by using Maple 18. Graphical simulations divulge that varying the wave velocity affects the dynamical behaviors of the model. In summary, this research adds to our knowledge on how the perturbed GI equation with spatio-temporal dispersion behaves. The obtained soliton solutions and the methods offer computational tools for further analysis in this field. This work represents an advancement in our understanding of soliton dynamics and their applications in photonic systems.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" 22","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135241055","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}

{"title":"Existence and multiplicity of solutions for the Cauchy problem of a fractional Lorentz force equation","authors":"Xiaohui Shen, Tiefeng Ye, Tengfei Shen","doi":"10.1186/s13661-023-01793-4","DOIUrl":"https://doi.org/10.1186/s13661-023-01793-4","url":null,"abstract":"Abstract This paper aims to deal with the Cauchy problem of a fractional Lorentz force equation. By the methods of reducing and topological degree in cone, the existence and multiplicity of solutions to the problem were obtained, which extend and enrich some previous results.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"2005 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135813277","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}

{"title":"Numerical solution of Bratu’s boundary value problem based on Green’s function and a novel iterative scheme","authors":"Junaid Ahmad, Muhammad Arshad, Kifayat Ullah, Zhenhua Ma","doi":"10.1186/s13661-023-01791-6","DOIUrl":"https://doi.org/10.1186/s13661-023-01791-6","url":null,"abstract":"Abstract We compute the numerical solution of the Bratu’s boundary value problem (BVP) on a Banach space setting. To do this, we embed a Green’s function into a new two-step iteration scheme. After this, under some assumptions, we show that this new iterative scheme converges to a sought solution of the one-dimensional non-linear Bratu’s BVP. Furthermore, we show that the suggested new iterative scheme is essentially weak $w^{2}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>w</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -stable in this setting. We perform some numerical computations and compare our findings with some other iterative schemes of the literature. Numerical results show that our new approach is numerically highly accurate and stable with respect to different set of parameters.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"SE-6 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135411516","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}

{"title":"Existence and nonexistence of solutions for an approximation of the Paneitz problem on spheres","authors":"Kamal Ould Bouh","doi":"10.1186/s13661-023-01789-0","DOIUrl":"https://doi.org/10.1186/s13661-023-01789-0","url":null,"abstract":"Abstract This paper is devoted to studying the nonlinear problem with slightly subcritical and supercritical exponents $(S_{pm varepsilon}): Delta ^{2}u-c_{n}Delta u+d_{n}u = Ku^{ frac{n+4}{n-4}pm varepsilon}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mo>±</mml:mo> <mml:mi>ε</mml:mi> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> <mml:mo>:</mml:mo> <mml:msup> <mml:mi>Δ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>u</mml:mi> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>c</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mi>Δ</mml:mi> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>d</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mi>K</mml:mi> <mml:msup> <mml:mi>u</mml:mi> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:mfrac> <mml:mo>±</mml:mo> <mml:mi>ε</mml:mi> </mml:mrow> </mml:msup> </mml:math> , $u&gt;0$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>u</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:math> on $S^{n}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>S</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:math> , where $ngeq 5$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>5</mml:mn> </mml:math> , ε is a small positive parameter and K is a smooth positive function on $S^{n}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>S</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:math> . We construct some solutions of $(S_{-varepsilon})$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi>ε</mml:mi> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:math> that blow up at one critical point of K . However, we prove also a nonexistence result of single-peaked solutions for the supercritical equation $(S_{+varepsilon})$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mo>+</mml:mo> <mml:mi>ε</mml:mi> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:math> .","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"13 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135411642","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}

{"title":"Determination of rigid inclusions immersed in an isotropic elastic body from boundary measurement","authors":"Mohamed Abdelwahed, Nejmeddine Chorfi, Maatoug Hassine","doi":"10.1186/s13661-023-01788-1","DOIUrl":"https://doi.org/10.1186/s13661-023-01788-1","url":null,"abstract":"Abstract We study the determination of some rigid inclusions immersed in an isotropic elastic medium from overdetermined boundary data. We propose an accurate approach based on the topological sensitivity technique and the reciprocity gap concept. We derive a higher-order asymptotic formula, connecting the known boundary data and the unknown inclusion parameters. The obtained formula is interesting and useful tool for developing accurate and robust numerical algorithms in geometric inverse problems.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136013010","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}