19 papers
Sharp Time-Decay Estimates for Fractional Heat Semigroups Associated with Polynomial Anharmonic Oscillators
Julio Delgado, Vishvesh Kumar, Shyam Swarup Mondal
We investigate fractional heat semigroups generated by a class of anharmonic oscillators on of the form where and…
Fujita-type blow-up for inhomogeneous semilinear heat equations with regularly varying forcing
Vishvesh Kumar, Mohamed Majdoub
We develop a unified framework for Fujita-type blow-up of solutions to the inhomogeneous semilinear heat equation $$\partial_tu-Îu=|u|^p+\mathbf{w}(x), \qquad (t,x)\in(0,\infty)\t…
A positive ground state for a planar Choquard equation with mixed diffusion and critical exponential growth
Shaoxiong Chen, Sekhar Ghosh, Vishvesh Kumar +1
We study a two-dimensional Choquard equation driven by the mixed local and nonlocal operator , where the nonlinearity has critical exponential growth of Trudinger--…
Mixed local-nonlocal quasilinear problems with mixed interpolated Hardy potential
Yergen Aikyn, Sekhar Ghosh, Vishvesh Kumar +1
This paper addresses the existence of nontrivial solutions to a class of mixed local-nonlocal problems involving a mixed interpolated Hardy potential. We first establish a concentr…
Harnack inequality for superposition operators of mixed fractional order
Souvik Bhowmick, Sekhar Ghosh, Vishvesh Kumar +1
The main aim of this paper is to establish the Hölder continuity and the Harnack inequality for weak solutions to Dirichlet problems associated with superposition operators of mix…
Spectral analysis, maximum principles and shape optimization for nonlinear superposition operators of mixed fractional order
Yergen Aikyn, Sekhar Ghosh, Vishvesh Kumar +1
The main objective of this paper is to investigate the spectral properties, maximum principles, and shape optimization problems for a broad class of nonlinear ``superposition opera…