Bui Duc Nam, Bui Dai Nghia, Nguyen Anh Tuan
Abstract:
In this article, we study a non-local Love problem on unbounded domains where
the non-locality in the main equation is interpreted as a fractional Laplacian operator.
With various assumptions on the initial conditions, we derive several estimates for
mild solutions for the homogeneous source scenario. For the nonlinear problem,
we show the existence and uniqueness of a global mild solution.
In two cases, we obtain convergence results.
The first one states that the solution to the fractional Love equation converges
to the mild solution of the fractional wave equation according to a cross-section
radius parameter. The second result shows that solutions of the fractional
Love equation incorporating the fractional Laplacian operator converge to those of
the classical problem, involving the usual Laplacian, as the fractional orders
approach 1. This work is the first that we are aware of that deals with mild
solutions of Love equations on unbounded domains.
Submitted March 19, 2025. Published July 22, 2025.
Math Subject Classifications: 35L05, 35Q74, 35B40.
Key Words: Love type equation; global solution; regularity; behavior of solutions;
convergence
DOI: 10.58997/ejde.2025.76
Show me the PDF file (456 KB), TEX file for this article.
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Bui Duc Nam Ho Chi Minh City University of Industry and Trade Vietnam email: nambd@huit.edu.vn |
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Bui Dai Nghia Faculty of Mathematics and Computer Science University of Science, Ho Chi Minh City, Vietnam \email: dainghia2008@hcmuaf.edu.vn |
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Nguyen Anh Tuan Division of Applied Mathematics Science and Technology Advanced Institute Van Lang University, Ho Chi Minh City, Vietnam email: nguyenanhtuan@vlu.edu.vn |
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