TY - JOUR
T1 - Decay of mass for a semilinear heat equation with mixed local-nonlocal operators
AU - Kirane, Mokhtar
AU - Fino, Ahmad Z.
AU - Ayoub, Alaa
N1 - Publisher Copyright:
© Diogenes Co.Ltd 2025.
PY - 2025
Y1 - 2025
N2 - In this paper, we are concerned with the Cauchy problem for the reaction-diffusion equation ∂tu+tβLu=-h(t)up posed on RN, driven by the mixed local-nonlocal operator L=-Δ+(-Δ)α/2, α∈(0,2), and supplemented with a nonnegative integrable initial data, where p>1, β≥0, and h:(0,∞)→(0,∞) is a locally integrable function. We study the large time behavior of non-negative solutions and show that the nonlinear term determines the large time asymptotic for p≤1+α/N(β+1), while the classical/anomalous diffusion effects win if p>1+α/N(β+1).
AB - In this paper, we are concerned with the Cauchy problem for the reaction-diffusion equation ∂tu+tβLu=-h(t)up posed on RN, driven by the mixed local-nonlocal operator L=-Δ+(-Δ)α/2, α∈(0,2), and supplemented with a nonnegative integrable initial data, where p>1, β≥0, and h:(0,∞)→(0,∞) is a locally integrable function. We study the large time behavior of non-negative solutions and show that the nonlinear term determines the large time asymptotic for p≤1+α/N(β+1), while the classical/anomalous diffusion effects win if p>1+α/N(β+1).
KW - Critical exponent
KW - Large time behavior of solutions
KW - Mass
KW - Mixed local-nonlocal operator
KW - Semilinear parabolic equations
UR - https://www.scopus.com/pages/publications/105007234748
U2 - 10.1007/s13540-025-00417-1
DO - 10.1007/s13540-025-00417-1
M3 - Article
AN - SCOPUS:105007234748
SN - 1311-0454
JO - Fractional Calculus and Applied Analysis
JF - Fractional Calculus and Applied Analysis
ER -